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"... the shortest and best way between two truths of the real domain often passes through the imaginary one" (Jacques Hadamard)

Course Description

This is the second part of a two term course in Analysis (891 in the Fall, and 892 in the Winter). We will develop the fundamentals of complex analysis and explore several applications. We will take Weierstrass's approach, emphasizing the importance of power series. Here is a tentative list of topics: analytic functions (fundamental properties and local and boundary behavior), complex integration and complex differentiation, approximation by polynomials and rational functions, the Weierstrass convergence theorem, Cauchy’s theorem and consequences, zero counting and product formulae, several elementary functions (logarithm, fractional linear transformations, ...), the Riemann mapping theorem, harmonic functions, connections to Fourier analysis and oscillatory integrals.

Lectures

There will be two in-person lectures per week. Each lecture will be 80 minutes long. Here's the schedule:

• Tuesday 4:00pm - 5:20pm in Jeffery 101

• Thursday 2:30pm - 3:50pm in Jeffery 101

Textbook

• Complex Analysis by D.E. Marshall, Cambridge University Press, 2019.