• Course title: Experimental Physics 1a and 1b: Mechanics, Oscillations and Waves (CM, 1a) and TD(1b)
• Number of ECTS: 5
• Course code: BA_PHYS_GEN-28
• Module(s): Module 1.1
• Language: FR, EN
• Mandatory: Yes

Physique expérimentale 1a: Mécanique newtonienne, oscillations et ondes:

Le cours vise- à familiariser l’étudiant avec les principes et lois de la mécanique newtonienne- à l’apprendre à appliquer ces principes et lois à des phénomènes oscillatoires et ondulatoires- et à fournir à l’étudiant de manière ciblée des outils mathématiques indispensables en physique.

Physique Expérimentale 1b: TD (Travaux Dirigés)

:

L’étudiant est amené à- résoudre d’une manière autonome des problèmes en physique- appliquer les lois physiques- manipuler correctement les outils mathématiques indispensables en physique

Physique expérimentale 1a: Mécanique newtonienne, oscillations et ondes:

L’étudiant(e) ayant validé l’unité d’enseignement- maîtrise les principes et lois de la mécanique newtonienne- sait appliquer les lois de la mécanique newtonienne à des phénomènes oscillatoires et ondulatoires- arrive à résoudre des problèmes inconnus en relation avec la mécanique newtonienne et les phénomènes oscillatoires ou ondulatoires- réussit à manipuler les outils mathématiques indispensables en mécanique.Physique Expérimentale 1b : TD (Travaux Dirigés):L’étudiant(e) ayant validé l’unité d’enseignement- arrive à résoudre des problèmes inconnus en relation avec la mécanique newtonienne et les phénomènes oscillatoires ou ondulatoires- réussit à manipuler les outils mathématiques indispensables en mécanique newtonienne

Motion of point masses/kinematicsForces and Newton’s laws of mechanicsWork and (potential and kinetic) energyRelative motion (Galilei transformation, inertial system, Centrifugal and Coriolis forces)Conservation principles (momentum, angular momentum, energy)Dynamic properties of rigid bodies (center of mass, moment of inertia, Euler equations)Oscillations and resonance (harmonic oscillator)Wave equation and propagation of wavesPrinciple of HuygensInterference phenomenaDiffraction of waves

 

Experimental Physics 1a

Written exam during the exam session.The student has to answer comprehension questions and solve problems comparable to those treated in the exercise class.During the exam he/she can use a pocket calculator and any mathematical tool.Duration of the exam: 120 minThe exam is graded out of 20 A student is only allowed to take the written exam if he got a grade for Experimental Physics 1b at the end of the exercise class.Experimental Physics 1bThe participation in the exercise class is mandatory.Continuous assessment (12-13 assignments) and midterm test.The midterm test counts for 50% of the final grade for the exercise class.The exercise class is graded out of 20.Students who do not regularly participate in the TD  are excluded from the exercise class (after two absences without a valid excuse or three absences with a valid excuse) = valid excuse : deregistration from the course by the study programme administrator / without valid excuse: ABSNJ (unjustified absence) -> 1 attempt out of 2.

 

To be admitted to the final exam in Experimental Physics 1a the student must have completed the exercise class (Experimental Physics 1b) with a fin al grade.Calculation of the final grade for Experimental Physics 1a and 1b:Mark = (4xgradeexam+gradeTD)/5Retake exam offeredWritten examMark = (4xgradeexam+gradeTD)/5GradeTD = grade obtained at the end of the exercise class previously followed  by the student 

 

P. A. Tipler, G. Mosca: Physics for Scientists and Engineers, vol 1, Worth Publishers.D. Halliday, R. Resnick, J. Walker: Physik, Wiley-VCH.H. Benson: Physique 1: Mécanique, De Boeck Université.R. P. Feynman, R. B. Leighton, M. Sands: The Feynman Lectures on Physics, vol 1 and 2, Addison-Wesley (recommended for physicists).

• Course title: Experimental Physics 1c and 1d: Thermodynamics (CM, 1c) and TD(1d)
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-29
• Module(s): Module 1.1
• Language: EN
• Mandatory: Yes

Understand the fundamental concepts and the broad impact of the three principles of thermodynamics.

The student will be able to understand how to describe the complex phenomena occurring during thermodynamic transformations in terms of fundamental quantities.

Introduction: statistical approach to thermodynamics quantities; pressure and temperature; thermometers; kinetic theory of ideal gasses; temperature and internal energy; work and heat; conduction, convection, thermal radiation; heat capacity and specific heat; phase transitions. First Principle of Thermodynamics: adiabatic processes; free expansion of an ideal gas; quasi-static processes; isochoric and isobaric processes; isothermal processes; polytropic processes; thermodynamic cycle; heat engines and refrigeration cycles. Second Principle of Thermodynamics: Carnot theorem and Carnot Cycle; efficiency of a cycle; Clausius theorem; Entropy and third Principle of thermodynamics: Gibbs plane (TS); entropy in ideal gasses; entropy in solids and liquids; irreversible processes; statistical meaning of entropy.

Task 1: Written exam during the exam sessionTask 2: 3 evaluated exercise sheets. The completion of at least 2 sheets is mandatory in order to be admitted to the exam.Assessment rules: For the written exam the students are allowed only a non-programmable calculator.Assessment criteria: The written exam counts for the full evaluation. The performance in the exercise sheets will be considered as a bonus/malus of 1 point.Retake exam offered

Written exam. Still the admission is subject to the completion of 2 completed exercise sheets.

The lecturer provides notes for the course, but any fundamental Physics textbook aimed at undergraduate students will also work.

• Course title: BPHY Lab classes 1
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-2
• Module(s): Module 1.2
• Language: EN
• Mandatory: Yes

The students get to know physical laws and relations by conducting experiments.

•Consolidation of the knowledge gained in the theoretical undergraduate courses.•Getting skills in experimental physics.•Learning how to deal with experimental errors.•Learning how to write scientific reports.•Evaluate experimental data with the computer.

The students work in groups of two or maximum three persons during the experimental sessions. They conduct at least eight physical experiments from the following list:• Error Calculus• Dynamics of rigid bodies• Measurement of the gravitational acceleration• Interference and diffraction• Optical prims• Optical instruments• Newton’s rings• Specific charge of the electron• Stationary waves• Oscilloscope• Coupled pendulaFor each experiment, each group must write a report which is graded.Twice the semester, the students must pass an oral exam.

Continuous evaluation:

The final mark consists of •Evaluation of the conduction of the practical works during the sessions and evaluation of the reports for each experiment (33.3%)Each of the 8 reports must be graded with at least 10/20 in order to pass the course. The students have the possibility to resubmit improved versions of reports if grading is too low. •Evaluation of two oral exams during the semester (66.7%)Retake exam is not possible (continuous evaluation). 

If students fail the course, they have to register to the course the following year.

Support / Arbeitsunterlagen / Support:

Description of the experiments and additional information/literature made available on the courses’ Moodle page.

Littérature / Literatur / Literature:

Description of the experiments and additional information/literature made available on the courses Moodle page.

• Course title: Analysis 1
• Number of ECTS: 5
• Course code: F1_BAINFOR-6
• Module(s): Module 1.3
• Language: EN
• Mandatory: Yes

This course is an introductory analysis course, covering basics on numbers, sequences, and functions.The course aims to introduce students to these notions, including formal proofs, techniques and to give them necessary tools for the understanding of mathematics and the mathematical language of science.

At the end of the course the student will:-remember further mathematical knowledge. -apply analytic and critical thinking.-understand and practice deep mathematical concepts that will be used throughout their scientific career.-apply techniques from calculus to compute.

This course is an introductory analysis course, covering basics on numbers, sequences, and functions. There is both a calculus component (computations of limits of sequences, derivatives, function approximations, limits of sequences) and more theoretical analysis.This latter portion is sizeable part of the course where the students are introduced to proof techniques and the importance of rigorous arguments which are foundational and transversal in mathematics and science.

Assessment modality: Combined assessmentAssessment tasksTask 1: Written exam (60%)Grading scheme: 20 points (0-20)Objectives: Test concepts learned during the yearAssessment rules: Students cannot use calculators, electronic devices, or notes.Assessment criteria: Graded out of 20 with points for each exerciseTask 2: Written exam (20%)Grading scheme: 20 points (0-20)Objectives: Test concepts learned during the yearAssessment rules: These are partial exams during the semester (there are several of them). Students cannot use calculators, electronic devices, or notes.Assessment criteria: Graded out of 20 with points for each exerciseTask 3: Take-home assignment (10%)Grading scheme: 20 points (0-20)Objectives: Practice conceptsAssessment rules: Students work from home and can use course materials.Assessment criteria: Graded out of 20 with points for each exerciseTask 4: Written exam (10%)Grading scheme: 20 points (0-20)Objectives: QuizzesAssessment rules: There are 2 mandatory quizzes. Students cannot use calculators, electronic devices, or notes.Assessment criteria: Graded out of 20 with points for each exerciseTask 5: Written exam – RETAKE (100%)Grading scheme: 20 points (0-20)Objectives: The final grade, in case of a retake exam, is based 100% on the exam grade. (Performance on quizzes, homework, midterms, and exercises is not taken into account.)Assessment rules: Students cannot use calculators, electronic devices, or notes.Assessment criteria: Graded out of 20 with points for each exercise

Course materialsSyllabus☒Yes☐NoRemarks:Literature list☒Yes☐NoRemarks:Course notesMoodle page☒Yes☐NoRemarks:https://moodle.uni.lu/course/view.php?id=322 

• Course title: Linear Algebra 1
• Number of ECTS: 5
• Course code: F1_BAINFOR-8
• Module(s): Module 1.3
• Language: EN
• Mandatory: Yes

Fundamental notions of Linear Algebra.

The students recall and are able:•To formulate the basic notions of linear algebra. •To solve small linear algebra problems by performing calculations and applying algorithms.•To understand small proofs and to look for examples and counterexamples.

Systems of linear equations and matrices; determinants; Euclidean vector spaces (especially in dimension 2 and 3); general vector spaces (linear independence, span, basis).

Assessment modality: Combined assessmentAssessment tasksTask 1: Written exam – Midterm exam 1 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 2: Written exam – Midterm exam 2 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 3: Written exam – Midterm exam 3 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 4: Written exam – Final exam (70%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The test is graded.Task 5: Oral exam – optional Grading scheme: 20 points (0-20)Objectives: Oral exam (in case of justified absence to >1 midterms or as additional evaluation in case of fraud suspicion)Assessment rules: Discussion with questions (theoretical questions and exercises)Assessment criteria: Correct and partially correct answers contribute positively to the grade.Task 6: Either final written exam (100%) or the same modalities as the regular students (to be selected by each retaking student at the beginning of each semester)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The test is graded.  

Syllabus☒Yes☐NoRemarks:Moodle pageLiterature list☒Yes☐NoRemarks:Moodle pageMoodle page☒Yes☐NoRemarks:https://moodle.uni.lu/course/view.php?id=324 Other, please specify:

• Course title: Mathematical methods 1
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-5
• Module(s): Module 1.3
• Language:
• Mandatory: Yes

Mathematical Methods for physics 1a:Provide the student with the necessary mathematical tools needed to do physics.Mathematical Methods for physics 1b: TD (Travaux Dirigés)Tutorial to practice the lecture. The students learn to – solve mathematical problems by themselves;- apply mathematical laws and theorems;- manipulate mathematical concepts;- get fluent with calculus techniques. 

The student learns the mathematical tools necessary to start solving problems of mechanics and electromagnetism. 

 The following tools will be introduced: 1.     Vectors and Matrices2.     Complex Numbers3.     Differentiation and Integration4.     Taylor series5.     Differential equations6.     3-dimensional differentiation and integration7.     Fourier series and Fourier transform8.     Introduction to Probability

 

Task 1: Written examAssessment rules: No electronic devices or notes are allowedAssessment criteria: The final exam counts for 100% of the final gradeRetake exam: YESRegistration required: NOFor the retake exam the same rules apply as for the final exam. 

 

Support: copy of the slidesLiterature: Klaus Weltner: “Mathematics for Physicists and Engineers” (German and English)Alan Jeffrey: “Mathematics for Engineers and Scientists” 

• Course title: Introduction à l'astronomie et à la géodésie
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-37
• Module(s): Module Electives 1.4 (2 ECTS required to close the module)
• Language: FR
• Mandatory: No

The objective of the course is to provide students with an understanding of celestial coordinate systems, the movement of the sun, the concept of time, azimuth determination, and techniques for determining position based on astronomical observations.

By the end of the course, students will achieve a basic understanding of celestial coordinate systems and their correlations with terrestrial coordinates, variations in celestial body coordinates, and time systems.

Gain an understanding of celestial coordinate systems, time systems, astronomical azimuth determination, and geodesy. Learn to navigate the sky, track time accurately, and understand the Earth’s shape and dimensions.

Task 1: Home-Assignment and Participation (30%)Assessment Rules: Reports must be submitted via Moodle within the stipulated timeframe. Active and constructive engagement in class activities, discussions, and collaborative projects is required. Assessment Criteria: Each exercise is graded out of 20, assessing depth of understanding, application of concepts, and overall quality of work.Task 2: Final Exam (70%) The final written exam assesses students’ comprehension of the topics covered throughout the semester.Retake exam offered – rules: The grading for the retake exam is entirely based on the written retake exam.

•Smart, W. M. (1977). Textbook on spherical astronomy. (R. M. Green, Ed.) (6th ed.). Cambridge: Cambridge University Press.•Mackie, J. B. (1978).  The elements of astronomy for surveyors •Muller, I. I. (1977). Spherical and practical astronomy as applied to geodesy. (2nd ed.) New York: Frederick Ungar Publishing Co.

• Course title: Programming for Physics
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-30
• Module(s): Module Electives 1.4 (2 ECTS required to close the module)
• Language: EN
• Mandatory: No

Efficiently implement common physics-related calculations using a computer, with an understanding of numerical constraints on accuracy and time.Become familiar with famous computational models for physical processes showing chaotic or complex dynamics.

A student should be able to: –  Write a python program…  …to describe the time-evolution of a dynamical system  …to solve a field equation on a grid  …to solve a multidimensional optimisation–  Describe the behaviour of complex or stochastic dynamical systems in a statistical way–  Present results graphically in each case.

Basic programming skills, with interactive python worksheets for plotting.This course is an introduction to both computation for physics, and computational physics: a training in the computer skills needed to implement common physics calculations, and an introduction to the types of physical models which require computational treatment.

Task 1: Weekly electronic submission of completed interactive notebooks, including computer code and graphical presentation and discussion of self-generated data.  Any student who feels that their continuous assessment is a poor reflection of their ability may request an exam.Assessment rules: Collaboration between students is encouraged, cut-paste plagiarism is discouraged by forfeiting marks for all parties with overly similar work. Work which is directly copied  from online or AI resources without understanding will be penalised also.Retake exam offered

Rules: If a student wishes to retake the course, they may do so by repeating the process of continuous assessment or by requesting to sit an exam. Any student who feels that their continuous assessment marks are a poor reflection of their ability may request an exam. The exam will take place at a computer (disconnected from the internet) and will consist of a series of short and simple computational physics programming challenges.

Please note that only students who have already attended the course will be able

to retake the exam, and those who have not attended will have to re-enrol the

following year.

Written notes are provided as part of the interactive material. These notes do not form a complete repository of knowledge needed to pass the course.

• Course title: Experimental Physics 2c and 2d: Optics (2c, CM) and TD (2d)
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-39
• Module(s): Module 2.1
• Language: EN
• Mandatory: Yes

The students get to know physical laws and relations by the lecture and accompanying demonstration experiments

Understanding of the basic principles of Geometrical and Wave Optics

• Fermat’s and Huygens’s principles• Reflection, refraction, lenses, (spherical) mirrors, prisms• Image formation• Optical instruments• Matrix method for geometrical optics• Optics of the atmosphere• Interference and diffraction, single, double and multiple slit• Fraunhofer and Fresnel diffraction• General treatment of diffraction, Fresnel zone plates, Babinet’s theorem• Polarization• Anisotropic media, birefringence• Origin of the refractive index• Fresnel equations• Reflectance, transmittance• LASER

Assessment:

Written final examWritten mid-Term ExamAssessment rules:Allowed during written exams: Simple calculatorNot allowed during written exam: Lecture notes, exercises, any type of computer, use of smart phone during exam

Assessment criteria:

1/3 Mid-term exam, 2/3 Final exam;  graded out of 20

Support:

Lecture Notes are uploaded on MoodleExercises are uploaded on Moodle, solutions are discussed during the TD sessionsLiterature:Electrodynamics and Optics – W. Demtröder (Undergraduate lecture notes in Physics)Optics – E. HechtPhysics – Tipler

• Course title: Experimental Physics 2a and 2b: Electromagnetism (2a, CM) and TD (2b)
• Number of ECTS: 5
• Course code: BA_PHYS_GEN-27
• Module(s): Module 2.1
• Language: FR, EN
• Mandatory: Yes

Familiarizing the student with the principles and laws of electromagnetismSensitizing the student to the certainty that Maxwell’s theory of electromagnetism results from nature observation and is based on reproducible experimental factsGuiding the student to apply the principles and laws of electromagnetism to solve problems 

After completion of the course, the student is expected- to set up Maxwell’s equations using experimental laws deduced from nature observation;- to exploit Maxwell’s equations to prove that light propagates in form of electromagnetic waves;- to understand and apply the laws of electromagnetism.

Loi de Coulomb, Champ et potentiel électriques, Loi de Gauss et applications, Condensateur, Energie du champ électrique, Diélectriques dans le champ électrique, Polarisation diélectrique, Champ de déplacementCourant électrique:Intensité du courant électrique, Densité de courant, Conductivité et résistivité, Loi d’Ohm, Résistance électrique, puissance électrique, Effet Joule, Equation de continuité, Courant de polarisation dans un diélectrique, Circuits électriques, Lois de KirchhoffChamp d’induction magnétique:Force de Lorentz et champ d’induction magnétique, Force de Laplace, Effet Hall, Sources du champ d’induction magnétique : lois d’Ampère et de Biot-Savart, Propriétés magnétiques de la matière, Magnétisation, Champ magnétique, Paramagnétisme et diamagnétisme, FerroélectricitéInduction électromagnétique:Lois de Faraday et Lenz, Courants de Foucault, Induction mutuelle et auto-induction, Energie du champ d’induction magnétique, Courant de déplacement, Equations de MaxwellCourant alternatif:Tension et intensité efficaces, Dipôles passifs, Puissance du courant alternatif, Résonance et anti-résonance électriques, Oscillations électriques amorties, TransformateurOndes électromagnétiques:Equations télégraphiques, Ondes électromagnétiques, Propagation de l’énergie électromagnétique et vecteur de Poynting, Dipôle de Hertz, Dipôles secondaires et diffusion, Dispersion et absorption

Experimental Physics 1b: TD (exercise class)Homework: assignments on a weekly basisMidterm test The regular participation in the exercise class is mandatory: students with more than two unexcused absences are excluded from the exercise class.Experimental Physics 1a: CM (lecture)Written examTo be admitted to the written exam, the student needs a grade in Experimental Physics 1b.Final grade:Written exam counts for 80%Take-home assignments and midterm test count for 10% respectively.

Syllabus

• Course title: Theoretical Physics 1 : Mechanics
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-8
• Module(s): Module 2.2
• Language: EN
• Mandatory: Yes

The objective of the course is to introduce the students to the basic concepts of theoretical physics by solving famous and beautiful problems such as the parabolic flight of a ball, planetary motion, or the movement of a gyroscope. The course will convey the beauty and elegance of the mathematical description of the physical world. And it prepares the ground for the understanding of more advanced subjects of theoretical physics.

Understanding the approach of theoretical physics to the qualitative and quantitative description of nature

Mastering the Newtonian, Lagrangian, and Hamiltonian formulations of classical mechanics in generating equations of motion

Analytical and numerical skills for the solution of problems in classical mechanics.

Classical mechanics is the first course in a series of theoretical physics courses (followed by electrodynamics, quantum mechanics and statistical physics). The course introduces the basic concepts and approaches how to describe physical phenomena in terms of mathematical equations (equations of motions, typically in the form of differential equations). It also gives some analytical and numerical “recipes” how to solve these equations in order to describe the motion of a mechanical system as a function of time.The course reviews first the concepts of Newtonian Mechanics. In the next step, we introduce the Lagrangian formulation of classical mechanics as an alternative – and more efficient – way to derive the equations of motion for systems under constraints. In the third step, the Hamiltonian formulation of classical mechanics is introduced in order to prepare the students for the transition to quantum mechanics (which will be needed for the description of the microscopic world).Contents:Newtonian Mechanics: Newton’s Laws, Equations of motion, momentum and energy conservation.Analytical and numerical approaches to the solution of differential equationsLagrangian Mechanics: variational calculus, Hamilton’s principle, Euler-Lagrange equations, systems with mechanical constraintsMovement of rigid bodies: rotations, angular momentum, inertia tensor, movement of the gyroscopeCentral force problems: planetary motion, Kepler’s lawsHamiltonian Mechanics: symmetries and conservation laws, Liouville’s theorem, Poisson brackets, outlook on the transition to quantum mechanics 

Midterm and final written and/or oral exam

Retake: written and/or oral exam

John R. Taylor, Classical Mechanics, University Science Books 2004

Herbert Goldstein, Classical Mechanics, Person New International Edition 2013

• Course title: Analyse et applications 2
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-9
• Module(s): Module 2.3
• Language: EN
• Mandatory: Yes

Introduce Riemann integration theory, linear ODEs and multivariable calculus, showing interesting applications to the physical world. Also, students’ rigorous and mathematical thinking will be encouraged.

Upon successful completion of the course, students will: -Compute primitives of the usual functions by direct computation or by applying the most suitable integration method. -Understand the geometric meaning of Riemann integrals and their close relationship with derivatives via the Fundamental Theorem of Calculus. -Be aware of the power of Ordinary Differential Equations to model phenomena of the real world, -Know and use elementary methods of integration to solve linear ODEs of order 1 and 2. -Acquire some geometric intuition on the space R^n and the functions defined on it, as well as of important operations such as partial derivatives or differentials. -Get the ability to determine and interpret critical points of functions of several variables and compute integrals in dimensions higher than one.-Manipulate sequences of numbers and determine whether they are convergent or divergent by applying classical convergence tests. -Understand and use appropriately the mathematical language, being able to develop and express rigorous arguments

This is a second course in Calculus or Analysis, where connections with other mathematical subjects will be explored. Besides studying the crucial concepts of Riemann integrals and sequences of numbers, this course should be regarded as an introduction to multivariable calculus and the theory of Ordinary Differential Equations that are essential to understand mathematically the physical world. Finally, a theme of this course will be to analyze the similarities and differences between functions of one-variable and several variables to grasp their key analytic concepts (continuity, differentiation and integration). 0. Some recalls on Taylor series and their expansions0.1. Taylor formula with remainder0.2. Taylor-Lagrange formula0.3. Taylor-Young formula0.4. Taylor series products0.5. Taylor series composed of two functions0.6. Taylor series quotients1. The Riemann integral 1.1. Motivation and definition. Properties1.2. Integration techniques (computation of primitives, change of variable, integration by parts)1.3. The Fundamental Theorem of Calculus1.4. The improper integral2. Introduction to Ordinary Differential Equations2.1. Linear Ordinary Differential Equations2.2. Elementary integration: separation of variables, exact, homogeneous equations.2.3. Theory of existence and uniqueness.3. Calculus in several variables3.1. Functions of several variables. Continuity.3.2. Derivatives in several variables. Limits and continuity. Partial derivatives. Gradient. Chain rule and changes of coordinates.3.3. Riemann integral in several variables. Fubini theorem. Change of variables: polar, cylindrical and spherical. The formula of change of variables. (If time permits)3.4. Applications. Critical points (maxima, minima, saddle points). Computation of areas and volumes.4. Sequences of numbers4.1. Definitions and properties.4.2. First notions of convergence.4.3. Some useful tests of convergence

There will be one written midterm exam (M) and a written final exam (F). The final grade will be the maximum between F and 0.2M+0.8F. Students who do not obtain at least 10, they will need to do a resit exam E. Then, their final grade will be E.  

Support / Literature

BibliographyBasic references:• Gu´erin, C.: Analyse et applications 2 pour physiciens et ing´enieurs (checkmoodle)• Marsden, J. E. and Tromba, A.: Vector Calculus. W. H. Freeman andCompany, 2011, https://uuwaterloohome.files.wordpress.com/2020/04/jerrold-e.-marsden-anthony-tromba-vector-calculus.pdf• Simmons, G. F.: Differential equations with applications and historicalnotes. CRC Press, 2017.• Spivak, M.: Calculus. Publish or Perish, 2008.Complementary references:• Boyce, W. E.; DiPrima, R. C.: Elementary Differential Equations andBoundary Value Problems. Wiley, 2001.• Coddington, E. A.: An introduction to Ordinary Differential Equations.Dover, 1961.• Hunter, J. K.: An Introduction to Real Analysis, https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf• Rudin, W.: Principles of Mathematical Analysis. McGraw-Hill, 1976.• Stewart, J.: Multivariable calculus. Cencage Learning, 2010.

• Course title: Linear Algebra 2
• Number of ECTS: 4
• Course code: F1_BAINFOR-14
• Module(s): Module 2.3
• Language: EN
• Mandatory: Yes

Fundamental notions of Linear Algebra

The students recall and are able:To formulate the basic notions of linear algebra.To solve small linear algebra problems by performing calculations and applying algorithms.To understand small proofs and to look for examples and counterexamples.

General vector spaces (base change); matrix spaces, matrix transformations;  Eigenvalues and Eigenvectors; complex vector spaces ; inner product spaces, orthogonality; quadratic forms; general linear transformations; if time permits, some applications of linear algebra.

Assessment modality: Combined assessmentAssessment tasksTask 1: Written exam – Midterm exam 1 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 2: Written exam – Midterm exam 2 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 3: Written exam – Midterm exam 3 (15%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The tests are graded. The average of the two best midterms counts as mark.Task 4: Written exam – Final exam (70%)Grading scheme: 20 points (0-20)Objectives: Written test with exercises.Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The test is graded.Task 5: Oral exam, optionalGrading scheme: 20 points (0-20), Objectives: Oral exam (in case of justified absence to >1 midterms or as additional evaluation in case of fraud suspicion)Assessment rules: Discussion with questions (theoretical questions and exercises)Assessment criteria: Correct and partially correct answers contribute positively to the grade.Task 6: Either final written exam (100%) or the same modalities as the regular students (to be selected by each retaking student at the beginning of each semester)Grading scheme: 20 points (0-20), Objectives: ​​Written test with exercises. In case of fraud suspicion, the ​exam can be replaced by an oral exam (as described in Task 5). Assessment rules: Only 6 pages of personal notes are allowed. No calculators.Assessment criteria: The test is graded.

Syllabus☒Yes  ☐NoRemarks:Moodle pageLiterature list☒Yes  ☐NoRemarks:Moodle pageMoodle page☒Yes  ☐NoRemarks:https://moodle.uni.lu/course/view.php?id=2456Other, please specify: 

• Course title: Mathematical methods 2
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-11
• Module(s): Module 2.3
• Language: EN
• Mandatory: Yes

The aim of the course is to familiarize the student with the mathematical methods necessary for the course in analytical mechanics as well as electrodynamics.

After the course, the student should have the necessary mathematical skills to be able to follow theoretical physics courses of the Bachelor in Physics, in particular mechanics and electrodynamics.

– Calculus (differentiation and integration) in different coordinate systems- Partial differential equations- Green’s functions- Calculus of variations- Vector spaces of functions

Task 1: Weekly homework assignmentAssessment criteria: Students must achieve 50% of available points, homework grade constitutes 50% of final grade for the lecture.Task 2: Written examAssessment criteria: Students must achieve 50% of available points, final exam grade constitutes 50% of final grade for the lecture.

Lecture notes will be provided via moodle, recommended literature will be mentioned in each chapter.

• Course title: Introduction to Geophysics: Learning to think like a scientist
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-42
• Module(s): Module Option 2.4 (2 ECTS required to close the module)
• Language:
• Mandatory: No

The module will develop your understanding of Earth. We will use MATLAB to explore the different types of geophysical data to understand the physical properties of the Earth. Students will learn how•Search the Web for different types of geophysical data•Use MATLAB for data analysis•Create 2D plots of time series data•Understand the mean, scatter, and trend of geophysical time series•Fit seasonal signals and calculate residuals•Use geophysical data to measure plate tectonic velocities and estimate natural hazards•Plot and interpret the pattern of seismicity globally in terms of plate tectonics•Determine their location on Earth using GNSS•Understand mass changes on Earth from satellite gravity observations.

Students that successfully complete this course will be able:•To understand why the Earth looks like it does•To understand why earthquakes and volcanoes occur where they do•To understand how to use GNSS to measure plate velocities•To understand how GNSS and satellite gravity can tell us about Earth

Class Outline: Questions to Explore• How do geophysicists approach problem-solving and analysis?• What is the step-by-step process of the scientific method in geophysics?• What roles and tasks are undertaken by geophysicists in their field?• In what ways can MATLAB be effectively used to enhance our understanding of Earth’s dynamics?• What fundamental principles define plate tectonics and its role in shaping the Earth’s surface?• Why do seismic activities like earthquakes and volcanic eruptions occur in specific geographical locations?• What is the significance of satellite geodesy in geophysical research, and how does it contribute to our understanding of Earth?• How does GNSS play a key role in investigating seismic hazards, and what insights can be gained from such studies?• Distinguish between absolute gravity and relative gravity, and understand their respective applications in geophysics.• Explore the methodologies involved in measuring mass changes from space and the reasons behind these measurements.• What is optical imaging, and how does it serve as a tool for comprehending Earth’s processes and features?• What key components constitute the water cycle, and how does it influence various Earth processes and ecosystems?

Task 1: Written exam during exam session (45%)Task 2: Home-Assignment and Project (45%)Assessment Rules: Submission of reports via Moodle within the stipulated timeframe.Assessment Criteria: Graded out of 20 for each exercise, assessing depth of understanding, application of concepts, and overall quality of work.Task3: Participation (10%)Assessment Rules: Active and constructive engagement in class activities, discussions, and collaborative projects.Assessment Criteria: Evaluation based on the frequency and quality of contributions, demonstrating a commitment to the learning process.

To be defined in the lecture as required.

• Course title: Logiciels mathématiques
• Number of ECTS: 3
• Course code: BA_MATH_GEN-13
• Module(s): Module Option 2.4 (2 ECTS required to close the module)
• Language: FR, EN
• Mandatory: No

The first part of the course will cover the basics of the LaTeX markup language.We will see how to use it to write a mathematical text, such as lecture notes or a Thesis, and to prepare slides for a presentation.In the second part we will focus on SageMath and other mathematical software to carry out computations. We will also briefly talk about computational complexity and how to write more efficient code.

The student who completes the course will be able to use the LaTeX markup language to write documents and prepare slide-based presentations and to use SageMath and other mathematical software to carry out computations.

LaTeX [1] is a markup language to write and format documents of any type. It is particularly well-suited for scientific documents, but it can be used for any type of document, including books, CVs and even presentation slides.It can be used together with a graphical front-end (such as TexMaker, TexStudio, Overleaf…) to immediately see the pdf output. The main advantage over a more classical word processor such as Microsoft Word, besides a much better support for writing mathematical formulas and theorems, is that in LaTeX “What you see is what you mean” [2]: by typing commands instead of visually changing the appearence of the text, the “compiler” will always try to produce an output that is faithful to what the user indicated, so the user does not have to manually adjust the result after every major modification.SageMath [3] is a free and open-source Mathematical software system which builds on top of many existing: NumPy, SciPy, matplotlib, Sympy, Pari/GP, GAP, R and many more. Thanks to it, all the features all these languages can be accessed from a common python-based interface.In practice, the SageMath “language” is almost identical to python, but it provides a complete set of libraries to deal with many mathematical objects and computations.https://en.wikipedia.org/wiki/LaTeXhttps://en.wikipedia.org/wiki/WYSIWYMhttps://www.sagemath.org/ 

Homework (3 assignments) count for 100% of the grade

Notehttps://doc.sagemath.org/html/en/tutorial/index.html 

• Course title: Experimental Physics 3 : Modern physics
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-12
• Module(s): Module 3.1
• Language: EN
• Mandatory: Yes

The course on modern physics describes the new physics, that was developed in the first half of the 20th century. As an experimental course, we will emphasise the experimental evidence that triggered the development of modern physics. The course lays the foundations for the rigorous treatment of quantum mechanics in the 4th semester.The course aims to clarify the fact, that physics is a science in evolution, where new observations may lead to completely new theories.

Students will -understand the challenges for classical physics and how they led to the development of the theory of special relativity and of quantum mechanics-understand the basic laws and principles of special relativity and of quantum mechanics, in particular, where they are counter-intuitive with respect to everyday experience-deal confidently with the laws and principles of basic atomic physics-can apply these laws to unknown problems

1. Einstein’s trains and elevators – relativity 2. Particles and waves – quantisation and uncertainty3. An introduction to quantum mechanics – Schrödinger’s equation4. Atomic physics – the periodic system of elements5. A short introduction to molecular physics

Task 1: participate in TD (tutorial) and submit homeworkTask 2: written midterm exam during the semesterTask 3: Oral final exam i n the exam period. To be eligible for the oral exam, the student has to participate in the TD (see above) and obtain at least 6/20 points in the midterm. Students who are not eligible for the oral exam, have to retake the course the following year.Students who are eligible for the final exam, but fail to obtain an overall grade of 10/20 can retake the exam without retaking the course.Assessment rules: task 1:  Prerequisite for final exam: presence in all TD sessions and attempt to do at least 2/3 of the homework problemstask 2:  first part: no resources, second part: any paper resource allowed, no devices that can connect to the internettask 3: Q&A, no detailed calculations or derivationsAssessment criteria:task 1: no grade giventask 2: 6/20 points is prerequisite for final exam. Weight for final grade: 1/3task 3: weight for final grade: 2/3Retake exam offeredRetake exam – rules: new oral exam.final grade: 1/3 midterm of previous semester + 2/3 new oral exam

Copies of the slides available on Moodle.Books:Paul Tipler, Ralph Llewellyn “Modern Physics” (in English and German)Randy Harris “Modern Physics”Stephen Thornton, Andrew Rex “Modern Physics for Scientists and Engineers”“The Feynman lectures on physics” (in English, French and German)                                                           https://feynmanlectures.caltech.edu Harris Benson “Physique” 3 (in English and French)Wolfgang Demtröder “Experimentalphysik” (in German)

• Course title: Theoretical Physics 2: Electrodynamics and Relativity
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-13
• Module(s): Module 3.2
• Language: EN
• Mandatory: Yes

Understanding the concepts of a field theory; Acquiring the mathematical and theoretical skills to describe electro-magnetic phenomena starting from the Maxwell Equations.

Besides a profound overview over the classical theory of electro-magnetism, the student will acquire the necessary knowledge to treat electrodynamic phenomena within atomic, solid-state, soft-matter physics and other advanced branches of physics and material sciences. The mathematical skills acquired will also serve later for the solution of problems in quantum mechanics.

1.)     Introduction to Electrostatics and Electrodynamics2.)    Maxwell Equations in Vacuum3.)    Boundary-Value Problems in Electrostatics4.)    Multipole Expansion5.)    Magnetostatics6.)    Electromagnetic waves, wave propagation, scattering, diffraction7.)    Electrodynamics in macroscopic media8.)    Special theory of relativity.

Midterm and final written and/or oral exam

Support / Literature:

D. Griffith, Introduction to Electrodynamics, Prentice-Hall (1991)R.J. Jelitto, Theoretische Physik 3: Elektroydynamik, Aula-Verlag (1987)J.D. Jackson, Classical Electrodynamics, Wiley & Sons (1999)

• Course title: BPHY Lab classes 2
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-14
• Module(s): Module 3.3
• Language: EN, FR, DE
• Mandatory: Yes

The students get to know physical laws and relations by conducting experiments.

•Consolidation of the knowledge gained in the theoretical undergraduate courses.•Getting skills in experimental physics.•Learning how to deal with experimental errors.•Learning how to write scientific reports.•Evaluate experimental data with the computer.

The students work in groups of two or maximum three persons during the experimental sessions. They conduct at least eight physical experiments from the following list:• Gyroscope• Speed of light• Mechanical Oscillator• Adiabatic coefficient• Van der Waals experiment• Surface tension• Hydrogen Atom• Interferometry• Millikan experiment• Dielectric propertiesFor each experiment, each group must write a report which is graded.Twice the semester, the students must pass an oral exam.

Continuous evaluation:The final mark consists of •Evaluation of the conduction of the practical works during the sessions and evaluation of the reports for each experiment (33.3%)Each of the 8 reports must be graded with at least 10/20 in order to pass the course. The students have the possibility to resubmit improved versions of reports if grading is too low. •Evaluation of two oral exams during the semester (66.7%)Retake exam is not possible (continuous evaluation).If the student fail the course, he will have to register to the course the following year.

Support / Arbeitsunterlagen / Support:Description of the experiments and additional information/literature made available on the courses’ Moodle page.Littérature / Literatur / Literature:Description of the experiments and additional information/literature made available on the courses Moodle page.

• Course title: Mathematical Methods 3
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-15
• Module(s): Module 3.3
• Language: FR, EN
• Mandatory: Yes

Introduction to the basic concepts of the complex analysis with applications to Fourier transforms, series and differential equations. Introduction to the basic mathematical framework of the quantum theory.

Integration of simple meromorphic functions, Fourier transforms, diagonalization of endomorphisms, notion of scalar product, series expansion.

Complex analysis, Complex integration, Cauchy and residue Theorems.Vector spaces in finite and infinite dimensionsFunctional spaces, Normed spaces, Hilbert spacesSturm-Liouville problem, orthogonal polynomials

Final exam: Written examAssessment rules: Student cannot use any notes nor electronic devicesAssessment criteria: Graded out of 20 Retake exam offeredwritten exam (same rules as the final exam)

Support / LiteratureSerie Schaum Mathematique : Analyse complexe, Algèbre linéaireByron and Fuller : mathematics of classical and quantum physics Karevski : Physique quantique des champs et des transitions de phase.

• Course title: Chemistry 1
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-16
• Module(s): Module 3.3
• Language: EN
• Mandatory: Yes

The objective of this course is to provide a foundational knowledge of chemistry which is useful for the study of physics. This is namely the physical properties of elements, the types of bonding they undergo, the types of compounds they form, as well as their reactivity. More precisely the following objectives are defined: 1. To understand atomic properties in terms of electron – nucleus interactions.2. To understand the bonding of atoms in terms of the number, geometry, type of bond, and types of matter.3. To understand when a chemical reaction will proceed in a forward direction or not4. To understand the general chemical trends in s, p, and d-block elements.5. To understand how to name organic molecules, understand their 3-dimensional nature, know when they will react, and to learn about four different reaction mechanisms.

A student who passes this course will be able to:-   explain the following trends in the periodic table: size, ionization energy, electron affinity, electronegativity, and polarizability enabling them to:-   know the properties of elements such as the physical state, ability – number – strength and types of bond likely to be formed with other elements-   know the likely geometry of molecules-   calculate lattice strengths enabling them to discuss physical properties of compounds-   calculate whether a given reaction will proceed or not and whether it is enthalpic or entropy driven-   understand the trends in s, p and d-block chemistry-   be able to name and draw basic organic molecules understanding their 3-d nature-   to be able to explain what factors control whether an organic reaction will happen or not and be able to see which of the most basic reactions is likely to occur if given a new scenario

• Atoms: History of atomic structure, Nucleo-synthesis, modern atomic structure, Bohr model leading to quantisation, electron orbital shapes and radial distribution function, quantum numbers, aufbau principle, Pauli principle, Hund’s rule of maximum multiplicity, principle, orbital shielding and penetration, effective nuclear charge, building the periodic table, atomic properties including atomic radii, ionization energies, electron affinities, polarizability• Molecular structure and Bonding: Lewis bonding, Octet rule, electronegativity, ionic bonding model, covalent quantum mechanical description for hydrogen, bond enthalpy, molecular orbital energy diagram for 1st row p-block allows to explain bond order ~bond enthalpy and length, VSEPR, valence bond approach• States of matter and properties of a solid: gas, liquid, solid (amorphous and crystalline), calculation of lattice enthalpy using Born Haber leading to melting points, thermal stability and solubility, band structure leading to electrical properties• Thermodynamics: Chemical potential, Gibbs free energy, enthalpy, entropy• Main group chemistry including Hydrogen, s, p, and d block, properties and trends, as well as simple compounds such as hydrides, halides, and oxides.• Organic chemistry: nomenclature, hybridization (sp, sp2, sp3), alkanes, conformational analysis of alkanes, chemic

Task 1: Oral exam of 30 minutes for students registered on Moodle. Assessment rules: During the exam the students are expected to answer orally and draw diagrams on a piece of paper. A basic periodic table will be provided. A range of questions will be asked covering the entirety of the course.Assessment criteria:A minimum of 10 from 20 is required to pass the class. 100% of the final grade comes from the oral exam.Students are expected to understand the material from the course and apply it to new situationsRetake exam offered– rules:Re-take is an oral exam of 30 minutes. The student does not need to attend lectures in the next semester, if they do not want to.

Support : livres, notes de coursLiterature : Shriver and Atkins, Inorganic Chemistry, 4th edition or newer, oxford university press. ISBN-10: 0199264635 Atkins, Physical Chemistry, 5th Edition or newer, oxford university press. ISBN-10: 0198557302 Vollhardt and Schore, Organic Chemistry, 2nd Edition or newer Lecture slides available on Moodle, as well as videos of the lecture if required

• Course title: Analyse 3
• Number of ECTS: 7
• Course code: BA_MATH_GEN-17
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: FR, EN
• Mandatory: No

Les étudiants ayant suivi avec succès le cours d’analyse 3 seront capables de : Manipuler correctement les séries de fonctions et séries entières en particulierAppliquer les résultats classiques de la théorie des fonctions de plusieurs variables réellesRésoudre des problèmes d’application simples

Dans ce cours, on diversifie et approfondit diverses connaissances et techniques de l’analyse mathématique. On s’intéresse à démontrer plusieurs théorèmes fondamentaux dans l’étude des fonctions de plusieurs variables, des équations différentielles et des suites de fonctions.

ProgrammeFonctions implicites et applicationsThéorie locale des équations différentielles ordinairesConvergence de suites de fonctionsSérie de puissancesL’exponentielle matricielleThéorème d’approximation de Stone-Weierstrass

Contrôle continu et examen écrit

Littérature W. Rudin: Principes d’analyse mathématique.Des notes de cours sont mises à disposition des étudiants.

• Course title: Analyse 3b
• Number of ECTS: 5
• Course code: BA_PHYS_GEN-38
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: EN
• Mandatory: No

To understand and use appropriately the mathematical language, identify the hypotheses and conclusions, as well as to develop and express rigorous arguments.To grasp new mathematical concepts building on previous ones (mainly from Analysis and Applications 1 and 2, as well as Linear Algebra). To introduce elements of Functional Analysis, emphasizing the notion and significance of Hilbert spaces.To study the relationship between real problems, their mathematical models in terms of Ordinary Differential Equations, and how to solve them using Fourier analysis.To introduce Fourier series and Fourier transforms by studying the key results and examples.To present some interesting applications of Fourier analysis to the real world. 

The student will understand the notion of Hilbert spaces and will learn the main examples and properties.The student will use bounded linear operators and learn the significance of the Riesz representation theorem.The student will be able to compute Fourier series of the usual functions and will be aware of their use to solve differential equations.The student will be able to compute Fourier transforms and convolutions of functions.

1.  ELEMENTS OF HILBERT SPACESNorms and distances. Bounded linear operators. Inner spaces. Hilbert spaces and main examples. Nice properties of Hilbert spaces: projections, Bessel inequality and orthonormality. Linear functionals. The Riesz representation theorem.2.  FOURIER SERIESConvergence of functions: pointwise, uniform and L^2-convergence. Definition of Fourier series. Computation of the Fourier coefficients. Main properties.3.  THE FOURIER TRANSFORMDefinition of Fourier transforms. Plancherel’s theorem. Convolution. The Heisenberg Uncertainty Principle.

Task 1: Written examsAssessment rules:  No electronic devicesAssessment criteria: 50% Midterms, 50% Final exam.Retake exam offered – rules:  Written exam 100%

Basic references:Applied Analysis, John K. Hunter & Bruno Nachtergaele, available at Nachtergaele’s webpage, 2000.Introductory Functional Analysis with Applications, Erwin Kreyszig, John Wiley & Sons, 1978, ISBN: 978-0471504597.Elementary Classical Analysis, Jerrold E. Marsden & Michael Hoffman, W. H Freeman, 1993, ISBN: 978-0716721055. Analyse 3b pour le BASI physique et ingénierie, Jean-Marc Schlenker, 2014, available at Schlenker’s webpage.Partial Differential Equations: An Introduction, Walter A. Strauss, John Wiley & Sons, 2008, ISBN: 978-0470-05456-7. Complementary references:A Course in Functional Analysis, John B. Conway, Springer-Verlag New York, 2007, ISBN: 978-0-387-97245-9. Fourier Analysis, Javier Duoandikoetxea, American Mathematical Society, 2001, ISBN: 978-0-8218-2172-5.Partial Differential Equations, Lawrence C. Evans, American Mathematical Society, 2010, ISBN: 978-0821849743.Real Analysis: Modern Techniques and their applications, Gerald B. Folland, John Wiley & Sons, 2007, ISBN: 978-0471317166.Fourier series, Fourier transforms, and function spaces: a second course in Analysis, Tim Hsu, American Mathematical Society, 2020, ISBN: 978-1470451455.A student’s guide to Fourier transforms (with applications in Physics and Engineering), J. F. James, Cambridge University Press, 2011, ISBN: 978-052117683 5. Introductory Functional Analysis with Applications, Erwin Kreyszig, John Wiley & Sons, 1978, ISBN: 978-0471504597. Lectures on the Fourier transform and its applications, Brad G. Osgood, American Mathematical Society, 2019, ISBN: 978-1470441913. An introduction to partial differential equations, Yehuda Pinchover & Jacob Rubinstein, Cambridge university Press, 2005, ISBN: 978-0521613231.Fourier analysis: an introduction, Elias M. Stein & Rami Shakarchi, Princeton University Press, 2003, ISBN: 978-069111384-5. 

• Course title: Programming for Physics
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-30
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: EN
• Mandatory: No

Efficiently implement common physics-related calculations using a computer, with an understanding of numerical constraints on accuracy and time.Become familiar with famous computational models for physical processes showing chaotic or complex dynamics.

A student should be able to: –  Write a python program…  …to describe the time-evolution of a dynamical system  …to solve a field equation on a grid  …to solve a multidimensional optimisation–  Describe the behaviour of complex or stochastic dynamical systems in a statistical way–  Present results graphically in each case.

Basic programming skills, with interactive python worksheets for plotting.This course is an introduction to both computation for physics, and computational physics: a training in the computer skills needed to implement common physics calculations, and an introduction to the types of physical models which require computational treatment.

Task 1: Weekly electronic submission of completed interactive notebooks, including computer code and graphical presentation and discussion of self-generated data.  Any student who feels that their continuous assessment is a poor reflection of their ability may request an exam.Assessment rules: Collaboration between students is encouraged, cut-paste plagiarism is discouraged by forfeiting marks for all parties with overly similar work. Work which is directly copied  from online or AI resources without understanding will be penalised also.Retake exam offeredRules: If a student wishes to retake the course, they may do so by repeating the process of continuous assessment or by requesting to sit an exam. Any student who feels that their continuous assessment marks are a poor reflection of their ability may request an exam. The exam will take place at a computer (disconnected from the internet) and will consist of a series of short and simple computational physics programming challenges.Please note that only students who have already attended the course will be ableto retake the exam, and those who have not attended will have to re-enrol thefollowing year.

Written notes are provided as part of the interactive material. These notes do not form a complete repository of knowledge needed to pass the course.

• Course title: Topologie générale
• Number of ECTS: 5
• Course code: BA_MATH_GEN-20
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: FR, EN
• Mandatory: No

Au terme du cours l’étudiant doit être à même demaîtriser les concepts de base de la topologie générale ainsi que les outils pour l’étude, la description et la construction des espaces topologiques et des applications continues ;appliquer les outils de la topologie générale pour résoudre des problèmes posés sur des espaces topologiques

Apprendre les fondements de la topologie générale au travers des propriétés de base des espaces topologiques et des fonctions continues.

ProgrammEspaces topologiques, bases, intérieur, adhérence, frontière, application continue, topologie produit, topologie induite, espaces métriquesConnexité, connexité par arcs, composantes connexes, points de coupuresCompacité, axiomes de séparations, nombre de Lebesgue et applicationsEspaces quotientsLemme d’Urysohn, Théorème de Tietze et applications…

Examen écrit et travail personnel durant l’année.

• Course title: Physics didactics 1
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-36
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: FR, DE, EN
• Mandatory: No

•découvrir la richesse de l’enseignement de la physique•planifier et vivre des situations d’enseignement en classe•planifier des expériences de démonstration•analyser ses propres performances pour mieux s’orienter dans son choix professionnel•comprendre l’enseignement de la physique dans différents ordres d’enseignement.

Connaître les multiples facettes de l’apprentissage et de l’enseignement de la physique et les défis posés à l’enseignant.

Students will get the opportunity to teach in a ‘real life’ situation in a secondary school class. Furthermore there are courses on how to prepare, student pre – and misconceptions, evaluative and formative assessment, practical work and latest multi media methods e.g. Chat GPT, online teaching pros and cons

Assessment is done by handing in a portfolio at the end of the semester.This portfolio documents the different course subjects, activities, lesson plans, teaching performance etc. Attendance is mandatory to fulfill the requirements and no ECTS will be given for non-attendance. Elements evaluated: regular attendance, participation, assignments, preparation, execution and analysis of practical partGraded to 20 marks.Assessment rules: portfolio has to be handed in by a deadline announced to the students Assessment criteria: Practical part : 50 %Courses, assignments, participation : 50% Retake exam not offered

 Notes de cours:G. de Vecchi, L’enseignement scientifique, Delagrave, 2002, ISBN: 2-206-08471-6H. Gudjons, Handlungsorientiert lehren und lernen, Klinkhardt, 2008, 2008, ISBN: 978-3-7815-1625-0Kirchner Girwidz Häußler, Physikdidaktik, Springer, 2001, ISBN: 3-540-41936-5H. Klippert, Methodentraining, Beltz 2005, ISBN: 3-407-62545-6A.B. Arons Teaching Introductory Physics, Wiley, 1996, ISBN: 978-04711-37078M. Reiss Understanding Science Lessons, Open University Press, 2001, ISBN: 978-0335-197699H.K. Mikalsis (Hrsg.) Physik Didaktik, Cornelsen Scriptor, 2006, ISBN: 378-3589221486Edited by J.Osborne and J. Dilon Good Practice in Science teaching, OUP 2010 ISBN: 978-033523858-3  

• Course title: Probabilités et statistique appliquée pour ingénieurs et physiciens 1
• Number of ECTS: 5
• Course code: BA_PHYS_GEN-17
• Module(s): Module Electives 3.4 (8 ECTS required to close the module)
• Language: EN
• Mandatory: No

Understand the concepts of randomness, probabilities and statistics.

A good handle of the concept of probability, uncertainty, descriptive statistics and discrete random variables, as well as know how to avoid the typical statistical mistakes.

The course will start with a motivation to know probability and statistics, in particular by showing its uses in everyday life and in particular in physics and engineering. We will then see descriptive statistics and how to avoid the typical statistical mistakes. Next we will lay out the basics of probability theory, (discrete) random variables, stochastic simulations, and finally draw a link to modern-day topics such as artificial intelligence and data science. 

Task 1: Written midterm examTask 2: Written final exam Assessment rules:The midterm concerns exercises as well as conceptual questions about the theory. The final exam only concerns exercises.Assessment criteria: Midterm counts for 5 points, Final exam for 15 points. Retake exam offeredRules: Exactly the same type of written exam like the final exam.

Slides that will be handed out before each course (except for the very first course).

• Course title: Theoretical physics 3 : Quantum mechanics
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-18
• Module(s): Module 4.1
• Language: EN, FR
• Mandatory: Yes

The main idea of the course is to teach students on using the mathematical formalism of quantum mechanics for solving different QM problems.

During this course the students get basic knowledge on quantum mechanics (QM), which is normally assumed for Bachelor students

Review of the classical lagrangian and hamiltonian mechanics: configuration space, least action principle, Legendre transform,Hamilton equations, Poisson Brackets, Liouville equation; -Double slit experiment: breakdown of classical mechanics and path-integral interpretation of interference pattern. -History of quantum mechanics: black body problem, UV catastrophe, Rayleigh-Jeans and Planck distributions, photoelectric effect and Einstein interpretation, concept of photon, Hydrogen spectrum and Bohr model of the hydrogen atom, Compton effects, de Broglie wave mechanics, Schrödinger wave equation, Heisenberg matrix QM, Copenhagen interpretation of QM; -The conceptual and mathematical structure of QM: Hilbert space of quantum states and its properties, commutator of linear operators, algebra of quantum observables (hermitian operators), and its representation in Hilbert space (algebra of Hermitian operators), change of representation, and projectors on eigenspace of hermitian operators. Expectation value of an operator on a given state. Unitary evolution and Stone’s Theorem. Conceptual aspects of the uncertainty principle in QM for the canonical conjugate variable. -QM of 1D systems: stationary and time-dependent Schrödinger equation, eigenvalues and eigenstates of the Hamiltonian operator, degeneracy of eigenvalues, Node theorem, free particle on the real axis and in a finite domain with periodic boundary conditions. Plane waves, Fourier transforms, and change of representation between canonical conjugate variables. -1D Quantum Harmonic oscillator: eigenvalues and eigenstates of the Hamiltonian operators, Hermite polynomials, ground-state energy, and comparison with the classical harmonic oscillator. Creation/annihilation operators algebra; -QM of 2D and 3D systems: separation of variables in Schroedinger equation, angular momentum theory 2D and 3D rigid rotor, Hydrogen atom Hamiltonian and its eigenvalues and eigenstates (Laguerre Polynomials). Pauli Spin and exchange interactions. -Approximate methods: Time independent perturbation theory, Stark effect, Variational principle, Selection rules, Time-dependent perturbation theory, Fermi golden rule.The exercise course covers many mathematical demonstrations and applications of the arguments presented in the theoretical course.

The bibliography includes:- Stephen Gasiorowicz, “Quantum Physics”;- David J. Griffiths and Darrell F. Schroeter, “Introduction to Quantum Mechanics”;- J. J. Sakurai, “Modern quantum mechanics”; – “Quantum mechanics and path integrals”,R. Feynman and A. Hibbs

The bibliography includes:- Stephen Gasiorowicz, “Quantum Physics”;- David J. Griffiths and Darrell F. Schroeter, “Introduction to Quantum Mechanics”;- J. J. Sakurai, “Modern quantum mechanics”; – “Quantum mechanics and path integrals”,R. Feynman and A. Hibbs Welcome to our course! 🙂

• Course title: Advanced lab course (Lab course 3+4)
• Number of ECTS: 8
• Course code: BA_PHYS_GEN-19
• Module(s): Module 4.2
• Language: EN
• Mandatory: Yes

The students get to know physical laws and relations by conducting experiments.

•Consolidation of the knowledge gained in the theoretical undergraduate courses.•Getting skills in experimental physics.•Learning how to deal with experimental errors.•Learning how to write scientific reports.•Evaluate experimental data with the computer.

The students work in groups of two or maximum three persons during the experimental sessions. They conduct at least eight physical experiments from the following list:• Quantization• Heat conductivity• X-Rays• Crystallography• Magnetic properties of atoms (ESR, NMR)• Zeeman Effect• Thermal Machines• Mechanical properties• Optical tweezers• LASERFor each experiment, each group must write a report which is graded.Twice the semester, the students must pass an oral exam.

Continuous evaluation.The final mark consists of •Evaluation of the conduction of the practical works during the sessions and evaluation of the reports for each experiment (33.3%)Each of the 8 reports must be graded with at least 10/20 in order to pass the course. The students have the possibility to resubmit improved versions of reports if grading is too low. •Evaluation of two oral exams during the semester (66.7%)Retake exam is not possible (continuous evaluation).

Support:Description of the experiments and additional information/literature made available on the courses’ Moodle page.Literature:Description of the experiments and additional information/literature made available on the courses Moodle page.

• Course title: Chemistry 2
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-20
• Module(s): Module 4.3
• Language: EN, DE
• Mandatory: Yes

To make sure that the student knows all the hazards which are possible during the laboratory experiment that they are about to undertake.To make sure that the student understands what to do, and what the experiment is about, before actually doing the experiment, the student will be tested.Students must make an experimental report of what they have done, observed, and understood. A full description of the objectives is given in the laboratory guide which all students are given at the beginning of the course.(i) To learn how to carry out chemical experiments safely;(ii) learn how to report on chemical experiments;(iii) understand and carry out standard chemical experiments; (iv) introduce standard chemical procedures.

A student who successfully completes this course as instructed will be able to (i) research and assess the safety of the experiment that they are about to carry out (ii) write a scientific report including relevant abstract, aim, method, results, conclusion and bibliography respecting plagiarism rules (iii) use a weighing balance, pipette, various solution manipulations, thin layer chromatography, UV-VIS and IR spectroscopy amongst others (iv) quantify the concentration of a known chemical, assess the speed of a reaction, carry out an organic work up and be able to separate two compounds dissolved in the same solution.

There are five experiments carried out over six weeks.Before every experiment there is a preparation meeting.The five experiments are (1) acid – base titration (2) calibration curve for unknown concentration (3) organic experiment kinetics (4) organic acidic workup (5) chromatography.

Task: After every experiment the student must write a report including abstract, introduction, method, results and discussion, conclusion and bibliography. Assessment rules: Each report will be graded from 20 points. Each sub-section of the report has a certain number of points associated with it.Assessment criteria: To pass the TP class an average of above 10 points is required. Students are evaluated against strict criteria based on the presence of information, the quality of the information, the observations and calculations etc. A precise guide to what is expected is available to each student at the beginning of the class.

Own research.

• Course title: Introduction to Biological Physics
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-43
• Module(s): Module 4.3
• Language:
• Mandatory: Yes

Upon successful completion of the course, a student will have fundamental understanding of the topics covered during the course, including but not limited to:- basic units of life and cellular complexity- structure, dynamics and functions of units of life – mechanistic understanding of biological units leading to systems and processes – understanding biological systems using physical models (examples)- hierarchical and emergent organization of living systems

We are living in the “Age of Biology”, where quantitative approaches from Physics are playing an increasingly crucial role in decoding the intricacies of biological systems and their diversity of structure, dynamics and functions. This course will provide an introduction to the field of Biological Physics, and equip students to study biological systems and processes using basic tools and techniques from the domain of Physics.

Continuous evaluation:

On each tutorial session, the students take a quiz based on the topics covered during the lectures preceeding the tutorials. The students will have 5 such quizes over the course of the semester. The performance in the quizes will account for 80% of the final score in the semester.

At the end of the semester, the students will do a presentation (in groups of 2-3): this will account for 20% to the final score.

No specific textbook will be followed, though for each topic relevant references will be suggested. Students are encouraged to take lecture notes; in some cases printed reading materials will be distributed during the lectures. Students can optionally follow Physical Biology of the Cell by Phillips, Kondev, Theriot and Garcia (ISBN: 0815344503).

• Course title: Didactics for Physics 2
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-26
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language: EN
• Mandatory: No

découvrir la richesse de l’enseignement de la physique

planifier et vivre des situations de TP en classe

expérimenter différentes méthodes modernes d’enseignement

analyser ses propres performances pour mieux s’orienter dans son choix professionnel

évaluer la performance des élèves

comprendre l’enseignement de la physique au secondaire et secondaire technique

Connaître les multiples facettes de l’apprentissage et de l’enseignement de la physique et les défis posés à l’enseignant.

Engagement régulier, élaboration d’un portfolio personnel (pièces créées à partir des éléments traités en cours), présentation du portfolio

Notes de coursG. de Vecchi, L’enseignement scientifique, Delagrave, 2002, ISBN: 2-206-08471-6H. Gudjons, Handlungsorientiert lehren und lernen, Klinkhardt, 2008, 2008, ISBN: 978-3-7815-1625-0Kirchner Girwidz Häußler, Physikdidaktik, Springer, 2001, ISBN: 3-540-41936-5H. Klippert, Methodentraining, Beltz 2005, ISBN: 3-407-62545-6A.B. Arons Teaching Introductory Physics, Wiley, 1996, ISBN: 978-04711-37078M. Reiss Understanding Science Lessons, Open University Press, 2001, ISBN: 978-0335-197699H.K. Mikalsis (Hrsg.) Physik Didaktik, Cornelsen Scriptor, 2006, ISBN: 378-3589221486

• Course title: Introduction to Geophysics: Learning to think like a scientist
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-42
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language:
• Mandatory: No

The module will develop your understanding of Earth. We will use MATLAB to explore the different types of geophysical data to understand the physical properties of the Earth. Students will learn how•Search the Web for different types of geophysical data•Use MATLAB for data analysis•Create 2D plots of time series data•Understand the mean, scatter, and trend of geophysical time series•Fit seasonal signals and calculate residuals•Use geophysical data to measure plate tectonic velocities and estimate natural hazards•Plot and interpret the pattern of seismicity globally in terms of plate tectonics•Determine their location on Earth using GNSS•Understand mass changes on Earth from satellite gravity observations.

Students that successfully complete this course will be able:•To understand why the Earth looks like it does•To understand why earthquakes and volcanoes occur where they do•To understand how to use GNSS to measure plate velocities•To understand how GNSS and satellite gravity can tell us about Earth

Class Outline: Questions to Explore• How do geophysicists approach problem-solving and analysis?• What is the step-by-step process of the scientific method in geophysics?• What roles and tasks are undertaken by geophysicists in their field?• In what ways can MATLAB be effectively used to enhance our understanding of Earth’s dynamics?• What fundamental principles define plate tectonics and its role in shaping the Earth’s surface?• Why do seismic activities like earthquakes and volcanic eruptions occur in specific geographical locations?• What is the significance of satellite geodesy in geophysical research, and how does it contribute to our understanding of Earth?• How does GNSS play a key role in investigating seismic hazards, and what insights can be gained from such studies?• Distinguish between absolute gravity and relative gravity, and understand their respective applications in geophysics.• Explore the methodologies involved in measuring mass changes from space and the reasons behind these measurements.• What is optical imaging, and how does it serve as a tool for comprehending Earth’s processes and features?• What key components constitute the water cycle, and how does it influence various Earth processes and ecosystems?

Task 1: Written exam during exam session (45%)Task 2: Home-Assignment and Project (45%)Assessment Rules: Submission of reports via Moodle within the stipulated timeframe.Assessment Criteria: Graded out of 20 for each exercise, assessing depth of understanding, application of concepts, and overall quality of work.Task3: Participation (10%)Assessment Rules: Active and constructive engagement in class activities, discussions, and collaborative projects.Assessment Criteria: Evaluation based on the frequency and quality of contributions, demonstrating a commitment to the learning process.

To be defined in the lecture as required.

• Course title: Probabilités et statistique appliquée pour ingénieurs et physiciens 2
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-25
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language: EN
• Mandatory: No

The course is meant to present some advanced topics of probability theory, such as laws of large numbers and central limit theorems, and to illustrate them through several concrete examples. The instructor will then apply these notions in order to introduce and develop some basic concepts of statistical inference.  Le cours vise à présenter quelques sujets avancés de la théorie des probabilités, tels que les lois des grands nombres et les théorèmes centraux limites, et à les illustrer à travers plusieurs exemples concrets. On appliquera ensuite ces outils afin d’introduire et de développer quelques notions de base de l’inférence statistique.

At the end of the course, the student will (i) understand the significance and use of probabilistic limit theorems (law of large numbers, central limit theorem); (ii) be able to apply the limit theorems at Point (i) to a number of concrete examples; (iii) understand and be able to apply the basic concepts of statistics, such as parameter estimation, confidence intervals and hypotheses testing. A l’issue du cours, l’étudiant (i) aura compris la signification et l’utilisation des théorèmes probabilistes limites (loi des grands nombres, théorème central limite) ; (ii) sera capable d’appliquer les théorèmes limites du point (i) à un certain nombre d’exemples concrets ; (iii) comprendra et sera capable d’appliquer les concepts de base des statistiques, tels que l’estimation des paramètres, les intervalles de confiance et les tests d’hypothèses.

After having reviewed some foundational notions (discrete and continuous random variables, densities, distribution functions, moment computation) the course will introduce the student to some advanced topics in probability theory, connected, in particular, to laws of large numbers and central limit theorems. In the second part of the lectures, several fundamental notions of statistical inference will be defined and illustrated through a number of examples.

Written exam Examen écrit

Lecture notes prepared by the instructor.Notes de cours.

• Course title: Data Science and Machine Learning in Physics
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-24
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language:
• Mandatory: No

A student should be able to: – Design and query a database- Smooth and feature-extract data using filters in direct and Fourier space- Extract features from high-dimensional data using Principal Components Analysis- Identify structures in data by clustering- Write down a Bayesian belief network- Design and train a perceptron  for a classification task- Demonstrate an understanding of self-organisation during the training process- Demonstrate an understanding of error propagation in a deep learning engine- Apply kernel machines to train non-linear maps 

 Learning outcomes- Understand numerical data as defining a family of structures in spaces- Understand soft, probabilistic and bio-mimetic reasoning methods- Understand approximation of probability distributions by nonlinear models 

 Data science is looking for patterns in large data sets.Machine learning is developing or fitting nonlinear models of many parameters (which may require large data sets). Feature discovery:    – Fourier analysis & filters :            1 lesson    – Principal Components Analysis:  1 lesson     – Clustering algorithms:                 2 lessonsMachine Learning:    – Multilayer neural networks :       2 lessonsStatistical Modelling:    – Bayes’ rule:                                           1 lesson    – Properties of distributions:                2 lessons    – Probabilistic logic and contingency: 2 lessons 

ContinuousWeekly tasks are given out and assessed.  Tasks will include python programming assignments, preparation and discussion of plots and graphs, and writing of derivations.

 https://en.wikipedia.org/wiki/Dimensionality_reduction https://en.wikipedia.org/wiki/Cluster_analysis https://www.cs.toronto.edu/~hinton/absps/NatureDeepReview.pdf 

• Course title: Analyse 4b
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-22
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language:
• Mandatory: No

Initiation to partial differential equations. Mathematical understanding of the heat and wave propagation on finite and infinite domains.

Students who successfully followed the course Analysis 4b will be capable of:-Solving various types of partial differential equations (as first order PDEs, wave equation, and heat equation) and qualitatively interpreting the solutions.-Modeling various physical phenomena by partial differential equations.-Applying the knowledge to simple physical problems.

1. First order PDEs. Surfaces, vector fields, integrable curves. Method of characteristic curves for solving first order PDEs. Non-global solutions and shock waves.2.  Wave equation.D’Alembert solution of the wave equation on the whole line. External forcing and resonance. Causality and energy.3. Heat or diffusion equation.Physical interpretation. General solution on the whole line. Maximum principle and stability. Distributions.4. Boundary problems.Wave and diffusion equation on a finite string. Separation of variables. Dirichlet, Neumann, and Robin boundary condition. Physical interpretation.5. Fourier series.Sine, cosine, and full Fourier series. Application to the initial-boundary value problem. Convergence and Gibbs phenomenon.

Continuous assessment and final exam.

Support / LiteraturePartial Differential Equations: An Introduction, Walter A. Strauss, John Wiley & Sons, 2007.- Introduction to Partial Differential Equations, Peter J. Oliver, Springer, 2014.-Partial Differential Equations, Lawrence C. Evans, AMS, Providence, Rhode Island, 2010.Information after course registration 

• Course title: Logiciels mathématiques
• Number of ECTS: 3
• Course code: BA_MATH_GEN-13
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language: FR, EN
• Mandatory: No

The first part of the course will cover the basics of the LaTeX markup language.We will see how to use it to write a mathematical text, such as lecture notes or a Thesis, and to prepare slides for a presentation.In the second part we will focus on SageMath and other mathematical software to carry out computations. We will also briefly talk about computational complexity and how to write more efficient code.

The student who completes the course will be able to use the LaTeX markup language to write documents and prepare slide-based presentations and to use SageMath and other mathematical software to carry out computations.

LaTeX [1] is a markup language to write and format documents of any type. It is particularly well-suited for scientific documents, but it can be used for any type of document, including books, CVs and even presentation slides.It can be used together with a graphical front-end (such as TexMaker, TexStudio, Overleaf…) to immediately see the pdf output. The main advantage over a more classical word processor such as Microsoft Word, besides a much better support for writing mathematical formulas and theorems, is that in LaTeX “What you see is what you mean” [2]: by typing commands instead of visually changing the appearence of the text, the “compiler” will always try to produce an output that is faithful to what the user indicated, so the user does not have to manually adjust the result after every major modification.SageMath [3] is a free and open-source Mathematical software system which builds on top of many existing: NumPy, SciPy, matplotlib, Sympy, Pari/GP, GAP, R and many more. Thanks to it, all the features all these languages can be accessed from a common python-based interface.In practice, the SageMath “language” is almost identical to python, but it provides a complete set of libraries to deal with many mathematical objects and computations.https://en.wikipedia.org/wiki/LaTeXhttps://en.wikipedia.org/wiki/WYSIWYMhttps://www.sagemath.org/ 

Homework (3 assignments) count for 100% of the grade

Notehttps://doc.sagemath.org/html/en/tutorial/index.html 

• Course title: Analyse numérique pour ingénieurs et physiciens
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-23
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language: FR
• Mandatory: No

Voir “learning outcomes”

Au terme du cours, l’étudiant doit être à même de:•comprendre le rôle central de l’analyse numérique dans les sciences mathématiques pures et appliquées;•maitriser les notions et les algorithmes fondamentaux de l’analyse numérique (approximation de fonctions, résolution d’équations, calcul approché d’intégrales);•acquérir un raisonnement rigoureux et systématique, indispensable à l’analyse et à l’interprétation des objets étudiés en analyse numérique;•formuler et résoudre mathématiquement certains problèmes numériques modélisables au moyen de l’analyse mathématique et de l’algèbre linéaire

• Normes d’opérateurs• Approximation polynomiale• Résolution d’équations non linéaires• Résolution numérique des systèmes linéaires• Intégration numérique• Résolution numérique d’équations différentielles

Examen écrit

Des notes de cours ou des slides sont disponibles sur la plateforme Moodle

• Course title: Ecrire et présenter dans le contexte académique en français et allemand – Wissenschafliches Schreiben & Präsentieren auf Französisch und Deutsch
• Number of ECTS: 2
• Course code: LC_CAT-55
• Module(s): Module options 4.4 (10 ECTS required to close the module)
• Language:
• Mandatory: No

Les étudiants peuvent:

structurer et rédiger un mémoire de Bachelor

lire plus rapidement et avec une meilleure compréhension de textes académiques

résumer un article

***

Die Studierenden können:

Eine Bachelorarbeit strukturieren und verfassen

Schneller Lesen und wissenschaftliche Texte besser verstehen

Wissenschaftliche Artikel zusammenfassen

Les étudiants peuvent:

lire et évaluer un mémoire de Bachelor en allemand

lire plus rapidement et avec une meilleure compréhension de textes académiques

résumer un article en français

***

Die Studierenden können:

eine Bachelorarbeit auf Deutsch lesen und bewerten

Schneller Lesen und wissenschaftliche Texte besser verstehen

einen Artikel auf Französisch zusammenfassen

Ce cours offre l’opportunité de développer des techniques de rédaction et de lecture des écrits académiques en français et en allemand. Les différentes parties du cours sont enseignées en français et en allemand à partir d’une combinaison d’exercices, de travaux d’écriture, de discussions et de réflexion sur les normes académiques dans les deux langues. Nous allons couvrir les points suivants:rédaction du mémoire de Bachelorlecture et compréhension d’articles académiquesrésumé d’un articletechniques de lecture rapidestyle et grammaire académique***In diesem Kurs werden Ihnen die Techniken des wissenschaftlichen Schreibens auf Französisch und Deutsch vermittelt. Verschiedene Teile des Kurses werden auf Französisch und Deutsch unterrichtet und bestehen aus einer Kombination aus Übungen, Schreibaufgaben sowie Diskussion und Reflexion über die Normen des wissenschaftlichen Schreibens in beiden Sprachen. Folgende Inhalte werden behandelt:Verfassen einer BachelorarbeitLesen und Verstehen wissenschaftlicher ArtikelZusammenfassen von ArtikelnTechnik des schnellen LesensWissenschatlicher Stil und Grammatik

Les étudiants devront:

lire et évaluer un mémoire de Bachelor en allemand

résumer un article en français

***

Die Studierenden müssen

eine Bachelorarbeit auf Deutsch lesen und bewerten

einen Artikel auf Französisch zusammenfassen

Support / Arbeitsunterlagen / Support:

Les documents pour le cours seront accessibles sur Moodle / Die Unterlagen zum Kurs werden auf Moodle gestellt.

 

Littérature / Literatur / Literature:

Les documents pour le cours seront accessibles sur Moodle / Die Unterlagen zum Kurs werden auf Moodle gestellt.

 

• Course title: Condensed matter physics
• Number of ECTS: 6
• Course code: BA_PHYS_GEN-31
• Module(s): Module 5.1
• Language: EN
• Mandatory: Yes

The students will get an overview of condensed-matter physics by learning about the basic principles of solid-state-physics (electrons in materials, lattices, …) and soft-matter physics (viscosity, elasticity, …)

After successfully completing this course, the students will be familiar with the foundations of solid-state physics and soft-matter physics.

Solid-state physics: – Fermi gas, Fermi-Dirac statistics- Electrons in periodic potentials (nearly free electrons, tight binding)- Lattices (point groups, space groups, etc.)- Magnetism- SuperconductivitySoft matter physics:The course will specifically address the following topics:- main types of soft matter: liquid crystals, amphiphiles, colloids and polymers;- structural organization, self-organization and self-assembly;- inter-molecular/ -particle interactions (van der Waals attraction (and analysis by the Hamaker approach), hydrogen bonding, hydrophobic effect, electrostatic interactions);- phase transitions and order parameters;  – diffusion and effect of electric fields;- deformations, reorientation and flow;- experimental methods for investigating soft matter.

Solid-state physics

Task 1:

Students must hand in solutions to the homework assignments every week. Homework solutions will be graded, and students must present their solutions regularly during the exercise class. Students must reach more than 50% of points to pass.Task 2:The students need to pass the final written exam at the end of the semester. Students need to reach more than 50% of the points to pass.Assessment rules: Books, notes, devices, etc. are not allowed during the final exam. The students can work in groups in the homework assignments, but each student must submit individually.Assessment criteria: Final grade will be weighted average.

———————————————————————————————————————————————

Retake exam offered

If a student has passed the homework part, he/she can retake the exam (written exam) without redoing the homework assignments.

 

Soft-matter physics

Task 1

Mid-term examTask 2Attendance to TD classes and hand-in (not graded) homeworks for TD classes (to be solved by students on the board). Task 3Final exam(written)Assessment rules: Students need to use calculators, not connecting to online resources. No books or notes consultation.Assessment criteria: Total score out of 20(Mid-term exam 30% + activity in TD participation 10% + final exam 60%) ———————————————————————————————————————————————Retake exam offeredCombined evaluation (mid-term exam + final exam). Retake exam is offered with additional required pre-exam test in case the intermediate evaluation was below threshold and the student had sufficient participation to TD classes. Retake exam – rules: Students need to use calculators, not connecting to online resources (written test).Total score, sum between the following scores: 10% from the activity in TDs, written test (30%) – if any – and oral (60%), otherwise 90% oral exam.

Solid-state physics: N/A

 

Soft-matter physics

:

Support:

Lecture slides available on Moodle LiteratureMain course books:Introduction to Liquid Crystals: Chemistry and Physics, by Peter J. Collings, Michael Hird, CRC Press, ISBN-13: 9780748404834 – CAT# TF1996“An Introduction to Interfaces & Colloids; The bridge to Nanoscience” by John C. Berg, World Scientific Press, ISBN-13: 978-981-4293-07-5Other books:The Physics of Liquid Crystals by P.G. de Gennes, J. Prost, Oxford University Press, ISBN-13: 978-0198517856“Intermolecular And Surface Forces” by Jacob Israelachvili, Academic Press, ISBN: 0123751829

• Course title: Continuum mechanics
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-32
• Module(s): Module 5.1
• Language: EN
• Mandatory: Yes

Given that this is a short introductory course and that continuum mechanics is a vast subject, we will focus on three key objectives: (1) give an understanding for when continuum descriptions of matter (solid or fluid) are appropriate and provide acquaintance with the key tools; (2) describe and analyze deformations of elastic solids; (3) describe and analyze fluid flow, free as well as on surfaces and confined inside channels

The student will understand key concepts like the continuum hypothesis; stress and strain in their different versions; Young’s modulus, Hooke’s law and Poisson’s ratio;  Cauchy’s stress principle; solid, fluid, liquid, gas, crystal, gel, glass and rubber states of matter; brittle, plastic, elastic, viscous and viscoelastic behavior; the continuity equation and conservation of mass; fluid particles, configurations and control volume; Eulerian and Laplacian descriptions of displacements; the material derivative; pressure and buoyancy; streamlines, streaklines and pathlines; Reynold’s transport theorem and the Navier-Stokes equations; the Reynolds number; the Bernoulli principle and the Venturi effect; laminar versus turbulent flow; fluid flow in pipes and the Hagen–Poiseuille equation; drag and lift and flow separation; d’Alembert’s paradox; interfacial and surface tension, capillary pressure and wetting; dripping, jetting and the Plateau–Rayleigh instability. In the process, the student will also get acquainted with tensor formalism and acquire practice in using it.

 1. Elastic deformation, its description and analysis using Cartesian tensors. 2. Kinematics: solids, fluids and the continuum hypothesis; Eulerian and Lagrangian descriptions.3. The Continuity and Navier–Stokes equations. 4. Relationship between velocity and pressure fields in flowing fluids; flow in pipes and channels. 5. From laminar to turbulent flow; drag and lift. 6. Interfacial/surface tension and capillary phenomena. 

Task 1: final oral examTask 2: mid-term written examAssessment rules: at the mid-term exam, the student can use an approved calculator and writing utensils but nothing else. At the oral exam, paper and writing utensils are provided and no further tools are necessary or allowed.Assessment criteria: 20% exercise class grade + 20% mid-term exam grade + 60% final exam grade.

 

Retake exam offered – rules:

Oral exam of the same type as the main exam. The score calculation is the same, using the score from the TD and Mid-term exam of the semester where the student followed the course. Only the new final exam score replaces the score of the first attempt at the final oral exam.

Most books dedicated to continuum mechanics are not suitable for a compact course like this one. The course thus draws material from a number of complementary books which each provide a stimulating perspective on a section of the field, such as:•Feynman Lectures on Physics, volume II•Michael Ruderman, Fluid Dynamics and Linear Elasticity: a first course in continuum mechanics•W. Michael Lai, David H. Rubin, Herhard Krempl, Introduction to Continuum Mechanics•Oscar Gonzalez, Andrew M. Stuart, A first course in continuum mechanics•Y.A. Cengel and J.M. Cimbala, Fluid Mechanics; fundamentals and applications•D.J. Tritton, Physical Fluid Dynamics•Pierre-Gilles de Gennes, Françoise Brochard-Wyart and David Quéré, Capillarity and Wetting PhenomenaEspecially the Cengel & Cimbala book is recommended as support, but all slides shown during the course will also be provided in PDF format.

• Course title: Theoretical physics 4 : Statistical physics
• Number of ECTS: 8
• Course code: BA_PHYS_GEN-33
• Module(s): Module 5.2
• Language: EN
• Mandatory: Yes

Assimilate the main concepts of statistical mechanics. Be able to reproduce the main derivations step by step.Use the concepts and tools from statistical mechanics to solve concrete problems.  

Assimilate the main concepts of statistical mechanics. Be able to reproduce the main derivations step by step.Use the concepts and tools from statistical mechanics to solve concrete problems.  

The course introduces the central concepts and tools of classical and quantum statistical physics, as well as basic concept in probability and information theory.The first half of the course will focus on the classical aspect and will be given by Massimiliano Esposito. The second half will focus on quantum aspects, spin systems, and elements of phase transition and will be given by Adolfo Del Campo.

Oral exam on the first part of the course (counts 50% of the final grade) on the week of November 4.Written exam on the second part of the course (counts 50% of the final grade) during the January exam session.

No retake exam offered: a

 student who has not passed the exam will have to repeat the course the following year and retake the exam. 

Note

(Support / Literature)

Statistical Physics of Particles by Mehran Kardar (Cambridge University Press, 2007)Equilibrium Statistical Physics by Michael Plischke et al. (World Scientific Book, 1994)Statistical Mechanics: A Set of Lectures Book by Richard Feynman (CRC Press, 1988)Lecture notes on selected topics

• Course title: Particle physics
• Number of ECTS: 4
• Course code: BA_PHYS_GEN-34
• Module(s): Module 5.2
• Language: EN, FR
• Mandatory: Yes

Acquisition des faits de base sur les noyaux et les particules élémentaires, connaissance du modèle standard des particules élémentaires.

Connaissances de base en physique de particules élémentaires.

I. Physique nucléaire1) Diffusion de Rutherford2) Propriétés des noyaux3)&4) Modèles nucléaires5)&6) Rayonnements nucléaires7)&8) Applications de la physique nucléaireII. Détecteurs et accélérateurs9) Détection des particules10) AccélérateursIII. Physique des particules11) Généralités12) Symétrie de jauge, groupe de Lorentz13) Symétries continues14) QCD15) Interactions faibles

Type of exam

: Written examAssessment rules: Students can use electronic devicesAssessment criteria: Final mark on 20 points.Retake exam offered – The mark of the retake exam replaces the insufficient mark of the first exam. Same type of examination.

YES / NOYES / NOThe mark of the retake exam replaces the insufficient mark of the first exam. Same type of examination.

N/A

• Course title: Literature seminar
• Number of ECTS: 5
• Course code: BA_PHYS_GEN-35
• Module(s): Module 5.3
• Language: EN
• Mandatory: Yes

The objective of the literature seminar is to introduce students to scientific literature relevant to the topics covered as part of the undergraduate curriculum; look up references; articulate ideas; and carry out discussions on the topic covered.

At the end of the literature seminar, students will be able to comprehend and understand scientific literature; and present relevant concepts and respond to questions pertaining to the literature covered.

The literature seminar aims to introduce student to relevant topics as a part of their undergraduate curriculum through scientific literature, with the possibility to include and discuss interdisciplinary topics in relation to core physics topics. The student is expected to work independently, with the possibility to meet and discuss with the seminar advisor periodically to clear doubts and receive clarifications on the chosen topic. At the end of the seminar period, the student holds a presentation the scientific paper covered, and responds to questions from the evaluators. The student is evaluated for their understanding of the scientific literature, presentation of the scientific paper, and answering questions from the evaluators. 

Literature review and seminar at the end of the semester.

N/A

• Course title: Big Data
• Number of ECTS: 4
• Course code: BPINFOR-82
• Module(s): Module Electives 5.4 (3 ECTS required to close the module)
• Language: EN
• Mandatory: No

The course is about (classical and new) techniques that are involved in the Big Data paradigm. The main goal is to spark the discussion about the Trade Offs between the classical data processing techniques and the upcoming ones for big data. In addition, students should get basic knowledge on how to automatically process and analyze huge amount of data.

On successful completion of this course, students are capable to:

demonstrate the ability to understand how to model a database system and the Trade Offs when the database goes big data, such as: consistency versus scalability and performance;

explain the database technologies for big data and analyze their pros and cons for proper usage;

design and develop big data solutions by adapting existing tools, designing new ones or a combination of both;

explain the concepts and the limits of the automated processing of data;

differentiate supervised and unsupervised learning and when one technique should be applied;

describe the concept of features and the importance of choosing discriminating ones;

select among basic algorithms for extracting information from a large data set and apply them.

The course is about (classical and new) techniques that are involved in the Big Data paradigm. The course combines two of the key dimensions of Big Data, namely:Part I – Design and development for big dataThe first part of the course will discuss databases and distributed computing algorithms for hosting and processing very large amounts of data:Conceptual modeling (ER Model), Relational Model (Algebra and SQL), Schema design (ER to Relational)Files and Access methods (except DHT)Distributed Databases, Data Warehouse and C-StoreNewSQL, Distributed Hash Tables, MapReduce, NoSQLThe main goal of the first part is to spark the discussion about the Trade Offs between the classical data processing techniques and the upcoming ones for big data.Part II – Data mining, classification and aggregationThe objectives of Part II are to guarantee that the students have a basic knowledge to automatically process and analyze huge amount of data. In particular, the two main objectives are to 1) extract information from a data set and 2) transform and store the data in a convenient way for further use (data mining, classification and aggregation):Classification (random forest, …)Clustering (k-means, …)Outlier and anomaly detection (local outlier factor, …)Regression (least squares, …)

Practical exercises, homework, continuous evaluation.

Literature: Relevant literature will be provided during the course.

• Course title: Introduction à l'astronomie et à la géodésie
• Number of ECTS: 2
• Course code: BA_PHYS_GEN-37
• Module(s): Module Electives 5.4 (3 ECTS required to close the module)
• Language: FR
• Mandatory: No

The objective of the course is to provide students with an understanding of celestial coordinate systems, the movement of the sun, the concept of time, azimuth determination, and techniques for determining position based on astronomical observations.

By the end of the course, students will achieve a basic understanding of celestial coordinate systems and their correlations with terrestrial coordinates, variations in celestial body coordinates, and time systems.

Gain an understanding of celestial coordinate systems, time systems, astronomical azimuth determination, and geodesy. Learn to navigate the sky, track time accurately, and understand the Earth’s shape and dimensions.

Task 1: Home-Assignment and Participation (30%)Assessment Rules: Reports must be submitted via Moodle within the stipulated timeframe. Active and constructive engagement in class activities, discussions, and collaborative projects is required. Assessment Criteria: Each exercise is graded out of 20, assessing depth of understanding, application of concepts, and overall quality of work.Task 2: Final Exam (70%) The final written exam assesses students’ comprehension of the topics covered throughout the semester.Retake exam offered – rules: The grading for the retake exam is entirely based on the written retake exam.

•Smart, W. M. (1977). Textbook on spherical astronomy. (R. M. Green, Ed.) (6th ed.). Cambridge: Cambridge University Press.•Mackie, J. B. (1978).  The elements of astronomy for surveyors •Muller, I. I. (1977). Spherical and practical astronomy as applied to geodesy. (2nd ed.) New York: Frederick Ungar Publishing Co.

• Course title: Business Software Systems
• Number of ECTS: 4
• Course code: BPINFOR-55
• Module(s): Module Electives 5.4 (3 ECTS required to close the module)
• Language: EN
• Mandatory: No

The students learn an overview and advantages of business software systems, especially ERP systems, and where these systems are used in business.

On successful completion of this course, students are capable to:

explain the role of business software systems in professional environments;

understand the purpose of business software systems, especially enterprise resource planning (ERP) systems;

clarify the role of business processes and apply basic techniques about modeling of business processes;

know the core business processes supported by business software systems;

understand the term Business Intelligence (BI) and know the components of a business intelligence system.

Overview of business software systemsIntroduction: business software systems, especially ERP-Systems, as basis of enterprise information processingClassification of business software systemsHistory, market review of ERP systemsArchitectures of ERP systems (client-server-architectures, layer models, interfaces)Business Process Management (BPM) and its relation to business software systemsBPM cycleModeling Techniques: BPMN, ARISMain business processes and their support by business software systems:Finance and accountingManufacturingSupply Chain ManagementCustomer Relationship ManagementManagement information systems / Business IntelligenceCase studies are analyzed in the class and assignments with practical exercises with BPM tools are given to the students.

Written examination (70%)

Control of homework/assignments (30%)

Literature:

Kenneth Laudon, Jane P. Laudon: Management Information Systems: Global Edition, 13th ed., Pearson Education, 2014.

K. Ganesh et. al.: Enterprise Resource Planning – Fundamentals of Design and Implementation, Springer International Publishing, 2014.

M. Dumas, M. La Rosa, J. Mendling, H. A. Reijers: Fundamentals of Business Process Management, 2nd ed., Springer. 2018.

B. Silver: BPMN Quick and Easy Using Method and Style: Process Mapping Guidelines and Examples Using the Business Process Modeling Standard, Cody-Cassidy Press. 2017

• Course title: Physics didactics 1
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-36
• Module(s): Module Electives 5.4 (3 ECTS required to close the module)
• Language: FR, DE, EN
• Mandatory: No

•découvrir la richesse de l’enseignement de la physique•planifier et vivre des situations d’enseignement en classe•planifier des expériences de démonstration•analyser ses propres performances pour mieux s’orienter dans son choix professionnel•comprendre l’enseignement de la physique dans différents ordres d’enseignement.

Connaître les multiples facettes de l’apprentissage et de l’enseignement de la physique et les défis posés à l’enseignant.

Students will get the opportunity to teach in a ‘real life’ situation in a secondary school class. Furthermore there are courses on how to prepare, student pre – and misconceptions, evaluative and formative assessment, practical work and latest multi media methods e.g. Chat GPT, online teaching pros and cons

Assessment is done by handing in a portfolio at the end of the semester.

This portfolio documents the different course subjects, activities, lesson plans, teaching performance etc. Attendance is mandatory to fulfill the requirements and no ECTS will be given for non-attendance. Elements evaluated: regular attendance, participation, assignments, preparation, execution and analysis of practical part

Graded to 20 marks.Assessment rules: portfolio has to be handed in by a deadline announced to the students Assessment criteria: Practical part : 50 %Courses, assignments, participation : 50% 

Retake exam not offered

 Notes de cours:G. de Vecchi, L’enseignement scientifique, Delagrave, 2002, ISBN: 2-206-08471-6H. Gudjons, Handlungsorientiert lehren und lernen, Klinkhardt, 2008, 2008, ISBN: 978-3-7815-1625-0Kirchner Girwidz Häußler, Physikdidaktik, Springer, 2001, ISBN: 3-540-41936-5H. Klippert, Methodentraining, Beltz 2005, ISBN: 3-407-62545-6A.B. Arons Teaching Introductory Physics, Wiley, 1996, ISBN: 978-04711-37078M. Reiss Understanding Science Lessons, Open University Press, 2001, ISBN: 978-0335-197699H.K. Mikalsis (Hrsg.) Physik Didaktik, Cornelsen Scriptor, 2006, ISBN: 378-3589221486Edited by J.Osborne and J. Dilon Good Practice in Science teaching, OUP 2010 ISBN: 978-033523858-3  

• Course title: Bachelor Thesis
• Number of ECTS: 27
• Course code: BA_PHYS_GEN-40
• Module(s): Module 6.1
• Language:
• Mandatory: Yes

The objective of the Bachelor thesis and presentation is to train final year undergraduate students about independent research activities (experimental and/or theoretical). The projects are mutually decided by the students with professors within the Department, after which the students undergo supervised training on the research questions and tasks. The students are encouraged to come up with their hypothesis and prove (or disprove) the hypothesis proposed. A second objective of the thesis is to train students on how to acquire, analyse, and present their data, both in written (bachelor thesis), as well as in oral forms (bachelor thesis presentation). The objective of the presentation is to prepare students about effective scientific communication using multimedia tools, oral presentation and follow up discussions.

 The Bachelor thesis and presentation will prepare students to carry out independent research projects, under supervision of senior researchers. The students will learn how to formulate a research question, acquire relevant datasets, analyse and represent the data, and provide a perspective to the thesis. The presentation allows students to learn about effective scientific communication, and methods to carry out scientific discussions and exchanges. 

1) The student identifies a professor with whom he would like to do the bachelor thesis. Once the professor and the thesis topic are finalized, the student should contact the SPA and the programme director confirming the choice of the topic, the name of the advisor, latest within the first week of the start of the semester or earlier if possible.2) Within a month of starting the bachelor thesis, the student should, after discussing with the thesis advisor, inform the SPA and the programme director about the scheduled date and time of the thesis presentation seminar. The presentation should take place latest during the exam period of the semester.3) The student should submit the final written version of the thesis latest within the first three weeks of the exam period. A copy of the thesis should be emailed to the SPA and the programme director.Any change in above plans (points 2 and 3), the student should first discuss with the thesis advisor, and upon agreement, communicate the same to the SPA and the course director

Evaluation of the Bachelor thesis will be based on: (i) independent research work carried out by the student; (ii) quality and content of the written thesisEvaluation of the Bachelor thesis presentation will be based on: (i) style and content of the thesis presentation, (ii) delivery and speech, (iii) response to follow-up questions and discussions. The Thesis Advisor is responsible for the evaluation, along with a co-evaluator (either a Professor or a senior scientist from the Dept. of Physics and Materials Science).Failing to pass the Bachelor Thesis and/or presentation would require that the student to repeats the thesis and/or the presentation. 

• Course title: Bachelor thesis presentation
• Number of ECTS: 3
• Course code: BA_PHYS_GEN-41
• Module(s): Module 6.1
• Language: FR, EN, DE
• Mandatory: Yes

The seminar provides a platform for students to present the results of their Bachelor’s dissertation and discuss these results with scientists.

The successful student will be able present and articulate their BPHY thesis work and results obtained using presentation slides. The presentation additionally aims to train students to carry out scientific discussions and Question-Answer sessions with experts and peers, in addition to allowing the evaluators assess the level of comprehension of the student.