Life of Fred: Complex Analysis

ISBN: 978-1-937032-61-6, hardback, 176 pages.

List of Topics Covered:

Arithmetic in the complex plane. Conjugates and absolute value. Polar form. Complex functions. Graphing. Limits and derivatives. Cauchy-Riemann equations. Holomorphic functions. Regions, open sets, connected sets. Paths. Analytic functions. Integration along a path. Fundamental Theorem of Complex Integration. Piecewise smooth paths. Paths with corners or cusps. Cauchy’s theorem. Closed paths. Simple paths. Cauchy–Goursat theorem. Trig functions, exponents, and logs in the complex plane. Argument of a polar complex function. Morera’s theorem. Three kinds of isolated singular points. Order of a pole. Proving L’Hospital’s rule in the complex plane. Meromorphic functions. Casorati-Weierstrass theorem. Picard’s great theorem. Cauchy’s formula. Jordan curve theorem. Liouville theorem. Proof of the Fundamental Theorem of Algebra. Taylor series and Laurent series. Residue theorem. Analytic continuation. Riemann Zeta function. Conformal Mappings. Homotopic paths. Harmonic functions.

The full 10-book Extra High School and College Math series includes:

1. Life of Fred: Logic
2. Life of Fred: Calculus Expanded Edition (freshman and sophomore year of college)
3. Life of Fred: Statistics Expanded Edition
4. Life of Fred: Life of Fred: Five Days of Upper Division Math: Set Theory, Modern Algebra, Abstract Arithmetic, Topology
5. Life of Fred: Abstract Algebra
6. Life of Fred: Linear Algebra Expanded Edition (junior year of college)
7. Life of Fred: Real Analysis
8. Life of Fred: Complex Analysis
9. Life of Fred: Numerical Analysis
10. Life of Fred: Metamathematics 

Life of Fred: Chemistry can also be read near the end of High-School or early College.