Life of Fred: Complex Analysis

Complex Analysis is the theory of functions of a single complex variable. (That is: Functions that map from complex numbers to complex numbers.) This is advanced undergraduate mathematics with applications to even more advanced mathematics, physics, and engineering.

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Life of Fred: Complex Analysis
(For Math Majors)

Complex Analysis is the theory of functions of a single complex variable. (That is: Functions that map from complex numbers to complex numbers.) This is advanced undergraduate mathematics with applications to even more advanced mathematics, physics, and engineering.

Topics include:

  • 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

Unlike most other Complex Analysis programs, this one also has:
• Fred’s scheduling issues
• Red Robin Hood

Click here to view a sample lesson (Opens in a new window or tab)

Life of Fred Complex Analysis is a hardcover textbook containing 176 pages. This book is not consumable. All answers are written on separate paper or in a notebook.

Number of Lessons: 24 Chapters. It is not broken up into daily lessons.