MATH-207(c) / 4 crédits

Enseignant: Moschidis Georgios

Langue: Anglais

## 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

Complex analysis

• Definitions and examples of complex functions.
• Holomorphic functions.
• Cauchy-Riemann equations.
• Complex integrals and Cauchy formulas.
• Series of Laurent.
• Residue theorem.

Laplace's analysis

• Laplace transforms.
• Fourier transforms.
• Applications to ordinary differential equations.
• Applications to partial differential equations.

## Keywords

Complex analysis, holomorphic functions, Fourier series, Laplace transform

## 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

 Office hours No Assistants Yes Forum No

## 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

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Analysis IV (for EL, GM, MX)
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: obligatoire
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Analysis IV (for EL, GM, MX)
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: obligatoire
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Analysis IV (for EL, GM, MX)
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: obligatoire
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Analysis IV (for EL, GM, MX)
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: obligatoire
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Analysis IV (for EL, GM, MX)
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: obligatoire

## Cours connexes

Résultats de graphsearch.epfl.ch.