MATH-207(c) / 4 credits

Teacher: Licht Martin Werner

Language: English

## Summary

This course is an introduction to the theory of complex analysis, Fourier series and Fourier transforms (including for tempered distributions), the Laplace transform, and their uses to solve ordinary and partial differential equations.

## 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.
• Applications to ordinary differential equations.
• Applications to partial differential equations.

## Required courses

Linear Algebra, Analysis I, Analysis II, Analysis III

## Important concepts to start the course

Important concepts to master

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

Exam written

## Bibliography

Bibliographie

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

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Analysis IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Analysis IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Analysis IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Analysis IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Analysis IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory

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