Schiz explains. TFKP 1.01. Contour integrals
This video introduces the concept of a contour integral of a function of a complex variable. To this end, it discusses paths and curves in the complex plane. It briefly touches on the geometric properties of complex numbers, Euler's formula, exponential form of a complex number, and trigonometric form of a complex number. The properties of contour integrals are discussed, and the Newton-Leibniz theorem is demonstrated for the complex plane. Of course, it also includes Cauchy's integral theorem and integral formula.
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00:00 Introduction
02:39 What is the path?
05:40 Two Important Examples
12:57 Contour Integral
16:43 A Fundamental Example
23:27 Properties of the Contour Integral
28:49 The Newton-Leibniz Theorem in the Complex Plane
33:08 A Very Important Corollary
33:40 A Counterexample?
36:02 Homotopy Equivalence of Paths and Curves
41:20 Cauchy's Integral Theorem
44:52 Cauchy's Integral Formula
49:42 In the Next Episodes
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