Analysis IV (for EL, GM, MX)

Summary

This course serves as an introduction to the theory of complex analysis, Fourier series and Fourier transforms, the Laplace transform, with applications to the theory of ordinary and partial differential equations. These tools play an integral role in most branches of science and engineering.

Content

Keywords

Complex analysis, holomorphic functions, Fourier series, Laplace transform

Learning Prerequisites

Required courses

Linear Algebra, Analysis I, Analysis II, Analysis III

Important concepts to start the course

• Usual derivatives and derivation rules
• Common primitives and integration techniques (integration by parts, substitution)
• Taylor series and analytic functions
• Complex numbers (definitions, Euler's identity, complex exponential)
• Fourier series and transforms
• Linear differential equations

Learning Outcomes

By the end of the course, the student must be able to:

• State the fundamental properties of holomorphic functions and the Laplace and Fourier transform.
• Use these properties to solve an array of problems.
• Choose the appropriate set of tools to address questions involving ordinary and partial differential equations.

Transversal skills

• Assess progress against the plan, and adapt the plan as appropriate.
• Demonstrate the capacity for critical thinking
• Demonstrate a capacity for creativity.
• Access and evaluate appropriate sources of information.

Teaching methods

2h lectures + 2h exercises

Expected student activities

Active participation in the regular classes, working on the problem sheets before the exercise sessions.

Assessment methods

Written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Resources

Bibliography

B. Dacorogna et C. Tanteri, Analyse avancée pour ingénieurs, PPUR 2018.

Resources at the library:

http://library.epfl.ch/en/beast?isbn=2-88914-565-4

Moodle Link

• https://go.epfl.ch/MATH-207_c