SJTU College: Complex Analysis
· Prerequisites: Calculus
· Credit: 4 credits
· Textbook: Complex Analysis (T.W. Gamelin)
· Background and Goals: This course is an introduction to the theory of complex valued functions of a complex variable. Fundamental ideas and rigorous proofs will be emphasized. Students are expected to understand the classical theory of complex analysis from the analytic, algebraic and geometric point of view. The prerequisite of a course in advanced calculus is essential. Some background in algebra and geometry is preferred.
· Content: Topics to be covered include: complex numbers, analytic functions, maximum principle, Cauchy’s theorem, Liouville’s theorem, power series, isolated singularities, residues, Rouche’s theorem, Schwarz lemma, Poisson integral and the Riemann mapping theorem. This roughly corresponds to the following material from Gamelin: Chapter I, Chapter II, Sections III.1-5, Sections IV. 1-6, Chapter V, Sections VI. 1-4, Sections VII. 1-4, Sections VIII. 1-2, Chapter IX, Sections X. 1-2, Sections XI. 1-2.