Complex Analysis - I

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About the course




This is an introductory course in Complex Analysis [in preparation]. We assume that the reader is somewhat familiar with complex numbers, so after a brief introduction into complex algebra, differentiation an integration we switch to more advanced topics which are not so often encountered in more standard courses but are very important for practical applications of complex analysis in theoretical physics. The course consists of video lectures with a multitude of high--quality graphical animations and is supplemented by graded assignments (via EdX server). The material is fully available for the Patreon subscribers, while some part of it is freely accessible (see the links below).

Syllabus

Lecture 1: Algebra of complex numbers. Integration and differentiation of functions of complex variables.

Lecture 2: Cauchy theorem. Types of singularities. Laurent and Taylor series.

Lecture 3: Residue theory with applications to computation of complex integrals.

Lecture 4: Multivalued functions and regular branches.

Lecture 5: Analytical continuation and Riemann surfaces.

Lecture 6: Integrals containing multivalued functions.


Assignments

[
assignment-1.pdf] [assignment-2.pdf] [assignment-3.pdf] [assignment-4.pdf] [assignment-5.pdf] [assignment-6.pdf]

Books on Complex Analysis