This course in Complex Analysis aims to teach students the fundamentals of complex differentiability, holomorphic functions, power series, and complex integration. Students will learn about Cauchy-Riemann equations, Wirtinger derivatives, and Laurent series. The teaching method includes theoretical explanations, examples, and proofs. This course is intended for learners interested in advanced mathematics and theoretical physics.
Overview
Syllabus
Complex Analysis - Part 1 - Introduction.
Complex Analysis - Part 2 - Complex Differentiability.
Complex Analysis - Part 3 - Complex Derivative and Examples.
Complex Analysis - Part 4 - Holomorphic and Entire Functions.
Complex Analysis - Part 5 - Total Differentiability in ℝ².
Complex Analysis - Part 6 - Cauchy-Riemann Equations.
Complex Analysis - Part 7 - Cauchy-Riemann Equations Examples.
Complex Analysis - Part 8 - Wirtinger Derivatives.
Complex Analysis - Part 9 - Power Series.
Complex Analysis - Part 10 - Uniform Convergence.
Complex Analysis - Part 11 - Power Series Are Holomorphic - Proof.
Complex Analysis - Part 12 - Exp, Cos and Sin as Power Series.
Complex Analysis - Part 13 - Complex Logarithm.
Complex Analysis - Part 14 - Powers.
Complex Analysis - Part 15 - Laurent Series.
Complex Analysis - Part 16 - Isolated Singularities.
Complex Analysis - Part 17 - Complex Integration on Real Intervals.
Complex Analysis - Part 18 - Complex Contour Integral.
Complex Analysis - Part 19 - Properties of the Complex Contour Integral.
Taught by
The Bright Side of Mathematics
