# 20243 Complex Functions 1

**Credits**: 3 intermediate and 3 advanced credits in Mathematics

**Prerequisites**: none

Required: Infinitesimal Calculus I, Infinitesimal Calculus II, as well as having accumulated a total of at least 24 credits in Mathematics

Recommended: Linear Algebra I, Infinitesimal Calculus III

The course is an expanded version of the British Open University course *Complex Analysis* (1975), translated by Naomi Shaked-Monderer, and adapted by Eli Levin and Dov Monderer.

Complex function theory is one of the basic tools of advanced mathematical analysis with wide-ranging applications in many branches of Mathematics and Physics. Familiarity with this theory is necessary for all students interested in pursuing their studies in Mathematics, and is of interest to students of Computer Science and Physics.

**Topics**: The complex plane; Continuous functions; Differentiability; Integration; Cauchy’s theorem; Taylor series; Singularities; Laurent series; The residue theorem and its applications; Sequences and series of analytic functions; Analytic continuations; Conformal mappings; Riemann’s mapping theorem.

This is a year-long course; however, capable students may increase the pace and complete the course work by the end of the fall semester, or begin later, at any time prior to the beginning of the spring semester.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.