complex Analysis

Lecture 1: Complex Analysis (History of Complex Numbers.)

Lecture 2: Complex Analysis (How complex numbers appeared while solving algebraic equations?)

Lecture 3: Complex Analysis (Set of complex numbers.)

Lecture 4: Complex Analysis (Algebra of complex numbers.)

Lecture 5: Complex Analysis (Polar form of complex numbers.)

Lecture 6: Complex Analysis (Polar form in terms of Exponential function.)

Lecture 7: Complex Analysis (nth power and mth root of complex numbers using their polar forms.)

Lecture 8: Complex Analysis (Definition of DOMAINS.)

Lecture 9: Complex Analysis (Importance of DOMAINS.)

Lecture 10: Complex Analysis (Stereographic projection.)

Lecture 11: Complex Analysis (Complex valued functions of complex variables I.)

Lecture 12: Complex Analysis (Complex valued functions of complex variables II.)

Lecture 13: Complex Analysis (Complex valued functions of complex variables III.)

Lecture 14:Complex Analysis (Defining limits of complex functions.)

Lecture 15: Complex Analysis (Continuity of complex functions.)

Lecture 16: Complex Analysis (admissible and inadmissible functions.)

Lecture 17: Complex Analysis (differentiable/ analytic functions.)

Lecture 18: Complex Analysis (Cauchy Riemann equations)

Lecture 19: Complex Analysis (CR conditions are not sufficient)

Lecture 20: Complex Analysis (When do the CR conditions become sufficient?)

Lecture 21: Complex Analysis(Derivative of a function zero in a domain implies it is constant)

Lecture 22: Complex Analysis(Analytic to harmonic functions and vice versa)

Lecture 23: Complex Analysis (Level curves of real and imaginary parts of analytic functions)

Lecture 24: Complex Analysis (Polynomial functions.)

Lecture 25: Complex Analysis (Rational functions)

Lecture 26: Complex Analysis (Exponential function.)

Lecture 27: Complex Analysis (Trigonometric and hyperbolic functions.)

Summary lecture: Complex Integration 1

Summary lecture: Complex Integration 2

Summary lecture: Complex Integration 3

Summary lecture: Complex Integration 4

Summary lecture:Complex integration 5 (CAUCHY INTEGRAL FORMULA FOR DERIVATIVES)

Summary lecture:Complex integration 6 (CAUCHY INTEGRAL FORMULA TO COMPUTE REAL INTEGRALS)

Summary lecture:Complex integration 7 (CONSEQUENCES OF CAUCHY'S INTEGRAL FORMULA)

Summary lecture:Complex integration 8 (MAXIMUM MODULUS PRINCIPLE)