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ES_APPM 312: Methods of Applied Mathematics: Complex Variables

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Prerequisites

Multivariable Calculus

Description

This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics.

It is a basic tool in many mathematical theories. We will  cover complex numbers and their properties, differentiation of complex-valued functions, analytic functions and the Cauchy-Riemann conditions, elementary functions of a complex variable, both single-valued and multi-valued, integration of complex functions, the Cauchy integral theorem, the residue theorem, and applications to definite integrals. We will also discuss conformal mappings and a number of applications of complex analysis.