Objectives of Programme's Learning Outcomes

• Understand the fundamentals
• Demonstrate knowledge and understanding of mathematics suitable for the study of physics, and be able to use this mathematics in applications in the field of physics
• Undertake further study having already acquired and enhanced the necessary learning skills

Learning Outcomes of UE

Understand the theorical aspects of the course and use them in the context of exercices.
Understand the differences between real and complex analysis.

UE Content: description and pedagogical relevance

Notion of holomorphic function. Cauchy-Riemann equations.
Integration of a complex function along a path. Cauchy Theorem.
Power series. Taylor and Laurent series.
Residue Theorem.

Prior Experience

Complex numbers: algebraic and trigonometric forms, complex plan, addition, multiplication, inverse, conjugate, de Moivre formula, solving polynomial equations,...
Real analysis: elementary functions (sin, cos, exp, ln,..), convergence of sequences and series of real numbers, one-variable differential and integral calculus, Taylor series for one-variable real functions.