MA 372

MA 372 - Complex Analysis

  1. The Algebra of Complex Numbers
    1. Introduction
    2. Complex conjugates and absolute values
    3. Geometric representation
    4. Roots of complex numbers

  2. Analytic Functions
    1. Introduction
    2. Elementary functions
    3. Complex derivative
    4. Properties of power series
    5. The Cauchy-Riemann equations
    6. Harmonic functions

  3. Complex Integration
    1. Introduction
    2. Contour integration
    3. Cauchy's Theorem
    4. Cauchy's integral formula
    5. Talor series expansion of an analytic function
    6. Maximum modulus principle

  4. Residue Theory
    1. Introduction
    2. Laurent expansion of an analytic function
    3. Classification of isolated singularities
    4. Cauchy Residue Theorem
    5. Applications of the Residue Theorem to the evaluation of real integrals
    6. The Argument Principle and Rouche's Theorem

  5. Optional Topics

Learning Outcome 1: The student will understand the basic properties of complex numbers and functions.

Learning Outcome 2: The student will understand the procedures of mapping by elementary functions.

Learning Outcome 3: The student will understand how to integrate complex functions using Cauchy's Residue Theorem.