Descriptif
In this course, we introduce vector and Fourier analysis from a hands-on, application-oriented perspective, in coordination with PHY104: Electromagnetism and Light. Vector analysis spans the differentiation and integration of vectors in two and three-dimensional space, eventually culminating with Green’s theorem in the plane and its higher-dimensional generalization, Stokes’ theorem. Changing gears, we introduce the concept of Fourier series, which give an approximation of periodic functions as an infinite sum of cosines and sines. We then use this tool to solve the wave equation on a finite domain. We conclude the course with a gentle introduction to Fourier transforms, viewed as a limit of Fourier series in the limit of infinite periodicity. Besides their intrinsic mathematical interest, these tools are widely used in Physics (Electromagnetism, Fluid mechanics, Quantum mechanics…).
Objectifs pédagogiques
The objectives of the course are:
- to introduce mathematical tools necessary for Physics courses, particularly PHY104, but also PHY202, PHY204, PHY205, MEC306
- to give students the opportunity to develop and practice their analytical calculational skills: derivation, integration, coordinate systems, vector algebra, differential equations...
- to emphasize the link between Mathematics and Physics
Diplôme(s) concerné(s)
Parcours de rattachement
Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vous devez avoir validé l'équation suivante : UE MEC_1F000_EP
FMA100, FMA101, FMA102, MEC100, MEC101
Format des notes
Numérique sur 20Littérale/grade américainPour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vos modalités d'acquisition :
The course is typically evaluated as follows
- continuous assessment (30% of final grade): short in-class tests (about 3-4 tests of 15-20 minutes) and/or homeworks
- final written exam (closed book, 2 hours, 70% of final grade)
Remedials consist of a 1-hour, closed book, written exam, or of an oral exam.
Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)La note obtenue rentre dans le calcul de votre GPA.
Programme détaillé
Session 1: Integration over multiple variables, surfaces and volumes. Cartesian, polar, cylindrical and spherical coordinate systems.
Session 2: Total differentials
Session 3: Gradient, divergence and curl
Session 4: Line integrals
Session 5: Green's theorem in the plane
Session 6: The divergence theorem in three-dimensional Euclidean space
Session 7: Stokes' theorem
Session 8: Fourier series, part I
Session 9: Fourier series, part II
Session 10: The wave equation
Session 11: Fourier transforms
Support pédagogique multimédia
