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MA 372
MA 372 -- Complex Analysis
- The Algebra of Complex Numbers
- Introduction
- Complex conjugates and absolute values
- Geometric representation
- Roots of complex numbers
- Analytic Functions
- Introduction
- Elementary functions
- Complex derivative
- Properties of power series
- The Cauchy-Riemann equations
- Harmonic functions
- Complex Integration
- Introduction
- Contour integration
- Cauchy's Theorem
- Cauchy's integral formula
- Talor series expansion of an analytic function
- Maximum modulus principle
- Residue Theory
- Introduction
- Laurent expansion of an analytic function
- Classification of isolated singularities
- Cauchy Residue Theorem
- Applications of the Residue Theorem to the evaluation of real integrals
- The Argument Principle and Rouche's Theorem
- Optional Topics
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