Goals

This course is a first course in complex analysis. It aims to be pratical and rigorous. Emphasis is put on power and significance of Cauchy's theorem. It also includes Fourier series.

Content

  1. Power Series
  2. Fourier Series
  3. Integration along paths and Cauchy theorem
  4. Holomorphic and Analytic Functions
  5. Cauchy's integral theorem and formula, consequences of Cauchy's theorem
  6. Singularities and Laurent's theorem
  7. Cauchy's residue theorem and applications to contour integration

In addition, a numerical application (using the software Matlab) on the Fourier series will be presented.

Table of contents

- Power Series - Fourier Series - Integration along paths and Cauchy theorem - Holomorphis and Analytic Functions - Cauchy's integral theorem and formula, consequences of Cauchy's theorem - Singularities and Laurent's theorem - Cauchy's residue theorem and applications to contour integration

 

  • Chapitre 0 : Complex numbers
  • Chapitre 1 : Power series. Holomorphis and Analytic Functions 
  • Chapitre 2 : Fourier Series
  • Chapitre 3 : Prelude to the Cauchy's theorem
  • Chapitre 4 : Cauchy's theorem
  • Chapitre 5 : Consequences of the Cauchy's theorem
  • Chapitre 6 : Singularities and Laurent's theorem
  • Chapitre 7 : Cauchy's residue theorem

 

Assessment method

The exam include two parts : Written (on exercises) and oral exam (on theory).

 

Consideration will be given to the area of ​​study of the student during the examination.

Sources, references and any support material

H.A. PRIESTLEY, Introduction to complex analysis, Oxford Sciences Publications, 1990.

Language of instruction

French
Training Study programme Block Credits Mandatory
Bachelier en sciences physiques Standard 0 5
Bachelier en sciences physiques Standard 2 5