Analysis of a Complex Kind

Video Lectures

Displaying all 36 video lectures.
I. Introduction to Complex Numbers
Lecture 1
History of Complex Numbers
Play Video		 History of Complex Numbers
Lecture 2
Algebra and Geometry in the Complex Plane
Play Video		 Algebra and Geometry in the Complex Plane
Lecture 3
Polar Representation of Complex Numbers
Play Video		 Polar Representation of Complex Numbers
Lecture 4
Roots of Complex Numbers
Play Video		 Roots of Complex Numbers
Lecture 5
Topology in the Complex Plane
Play Video		 Topology in the Complex Plane
II. Complex Functions and iteration
Lecture 6
Complex Functions
Play Video		 Complex Functions
Lecture 7
Sequences and Limits of Complex Numbers
Play Video		 Sequences and Limits of Complex Numbers
Lecture 8
Iteration of Quadratic Polynomials, Julia Sets
Play Video		 Iteration of Quadratic Polynomials, Julia Sets
Lecture 9
How to Find Julia Sets
Play Video		 How to Find Julia Sets
Lecture 10
The Mandelbrot Set
Play Video		 The Mandelbrot Set
III. Analytic Functions
Lecture 11
The Complex Derivative
Play Video		 The Complex Derivative
Lecture 12
The Cauchy-Riemann Equations
Play Video		 The Cauchy-Riemann Equations
Lecture 13
The Complex Exponential Function
Play Video		 The Complex Exponential Function
Lecture 14
Complex Trigonometric Functions
Play Video		 Complex Trigonometric Functions
Lecture 15
First Properties of Analytic Functions
Play Video		 First Properties of Analytic Functions
Lecture 16
Inverse Functions of Analytic Functions
Play Video		 Inverse Functions of Analytic Functions
IV. Conformal Mappings
Lecture 17
Conformal Mappings
Play Video		 Conformal Mappings
Lecture 18
Möbius Transformatios, Part I
Play Video		 Möbius Transformatios, Part I
Lecture 19
Möbius Transformatios, Part II
Play Video		 Möbius Transformatios, Part II
Lecture 20
The Riemann Mapping Theorem
Play Video		 The Riemann Mapping Theorem
V. Complex Integration
Lecture 21
Complex Integration
Play Video		 Complex Integration
Lecture 22
Complex Integration: Examples and First Facts
Play Video		 Complex Integration: Examples and First Facts
Lecture 23
The Fundamental Theorem of Calculus for Analytic Functions
Play Video		 The Fundamental Theorem of Calculus for Analytic Functions
Lecture 24
Cauchy's Theorem and Integral Formula
Play Video		 Cauchy's Theorem and Integral Formula
Lecture 25
Consequences of Cauchy's Theorem and Integral Formula
Play Video		 Consequences of Cauchy's Theorem and Integral Formula
VI. Complex Infinite Series
Lecture 26
Infinite Series of Complex Numbers
Play Video		 Infinite Series of Complex Numbers
Lecture 27
Power Series
Play Video		 Power Series
Lecture 28
The Radius of Convergence of a Power Series
Play Video		 The Radius of Convergence of a Power Series
Lecture 29
The Riemann Zeta Function and the Riemann Hypothesis
Play Video		 The Riemann Zeta Function and the Riemann Hypothesis
Lecture 30
The Prime Number Theorem
Play Video		 The Prime Number Theorem
VII. Laurent Series and the Residue Theorem
Lecture 31
Laurent Series
Play Video		 Laurent Series
Lecture 32
Isolated Singularities of Analytic Functions
Play Video		 Isolated Singularities of Analytic Functions
Lecture 33
The Residue Theorem
Play Video		 The Residue Theorem
Lecture 34
Finding Residues
Play Video		 Finding Residues
Lecture 35
Evaluating Integrals via the Residue Theorem
Play Video		 Evaluating Integrals via the Residue Theorem
Lecture 36
Evaluating an Improper Integral via the Residue Theorem
Play Video		 Evaluating an Improper Integral via the Residue Theorem