Complex Analysis

Functions of a complex variable: analyticity, Cauchy’s theorem, contour integration, Laurent series, residues, and conformal mappings. Where calculus becomes elegant.

Course Overview

Textbook

Churchill & Brown, Complex Variables and Applications

Chapters

TBD

Sections

TBD

Prerequisites

Calculus III, Real Analysis I

Target

Signal processing, quantum mechanics, advanced engineering mathematics

Status

Planned

Chapters will be scaffolded when this course becomes active.

Why This Course

  • Signal processing — Fourier and Laplace transforms live in the complex plane

  • Control theory — transfer functions, Nyquist diagrams, stability

  • Fluid dynamics — conformal mappings solve 2D flow problems

  • Number theory — the Riemann zeta function is complex analysis

  • Quantum mechanics — wave functions are complex-valued