Analysis III
Summary
Vector Calculus. Complex Analysis.
Content
Vector calculus:
- Line integral
- Surface integral
- Stokes, Green, and Gauss theorems
- Applications to partial differential equations
Complex analysis:
- Holomorphic functions
- Cauchy-Riemann equations, Cauchy's theorem
- Laurent Series
- Residue Theorem and Applications
Learning Prerequisites
Required courses
Analysis I, II, linear algebra for physicists.
Learning Outcomes
By the end of the course, the student must be able to:
- Elaborate the theory of line and surface integrals and its applications
- Develop the theory of complex functions and its applications
Teaching methods
Weekly Lectures and Exercise Classes
Expected student activities
Students are required to attend all the lectures and all the exercise classes. In addition, students are required to work through the entire list of exercises set every week.
Assessment methods
Written exam, one section to be written, one section multiple choice.
Supervision
| Office hours | Yes |
| Assistant.e.s | Yes |
| Forum | Yes |
Resources
Bibliography
Bernard Dacorogna, Chiara Tanteri, Analyse avancée pour ingénieur, EPFL Press 2018
See also:
Bernard Dacorogna, Analyse avancée pour mathématiciens:
Websites
- https://slsp-epfl.primo.exlibrisgroup.com/discovery/search?query=course_code,contains,%22MATH-201%202025-2026%22,AND&tab=41SLSP_EPF_MyInst_and_CI&search_scope=MyInst_and_CI&vid=41SLSP_EPF:prod&lang=fr&mode=advanced&offset=0
- https://www.epfl.ch/schools/sb/research/math/wp-content/uploads/2022/06/master1.pdf
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Analysis III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: obligatoire