Complex Analysis - A Full Course in One Video.. Brush up on CA in one afternoon

This video gives in a single video, a complete course in Complex Analysis that would be useful to students and professionals looking to apply complex analysis in various fields such as engineering, physics, and chemistry.

00:00:00 – Introduction and topics covered
00:01:20 – Why study complex analysis
00:02:45 – Transformation equation
00:11:18 – Linear transformations
00:15:56 – Magnification, rotation, and translation
00:20:58 – Non-linear transformation
00:30:00 – Differentiation and Cauchy-Riemann equations
00:47:58 – Harmonic Functions
00:55:58 – Contour integration
01:03:11 – Example of contour integration
01:12:00 – Cauchy-Goursat Theorem
01:22:00 – Example - Cauchy-Goursat Theorem
01:35:00 – Conformal mapping
01:40:52 – Example - conformal mapping
01:43:02 – Joukowsky Transformation
01:54:52 – Schwarz-Christoffel transformation - what it does
01:46:48 – Transformation of a simple polygon
02:03:01 – Transformation equation for Schwarz-Christoffel transformation
02:17:17 – Maclaurin series expansion of complex variable
02:20:54 – Example - Maclaurin series expansion
02:27:16 – Ratio test for convergence
02:31:27 – Example - Ratio test
02:41:23 – Radius of convergence
02:53:25 – Taylor series expansion of complex variable
02:57:15 – Example - Taylor series expansion
03:10:00 – What are singularities
03:11:54 – Poles
03:16:10 – Essential singularity
03:18:42 – Removable singularity
03:21:57 – Laurent series
03:28:11 – Derivation of residue term
03:46:29 – Calculation of residues from Laurent series
04:01:40 – Residues - shortcut for poles