Complex Analysis
N.B. Singh
This audiobook is narrated by a digital voice.
This audiobook, Complex Analysis, is a beginner-friendly guide that introduces you to the fascinating world of complex numbers and functions in a clear and simple way. Starting with the basics, it explains core concepts, like Cauchy’s integral formula and power series, using easy language and real-life examples to make the ideas more relatable. Ideal for students or anyone curious about complex analysis, this audiobook aims to build a solid understanding without overwhelming you with complicated terms or symbols, making it perfect for learning on the go.
Duration - 12h 57m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. This audiobook, Complex Analysis, is a beginner-friendly guide that introduces you to the fascinating world of complex numbers and functions in a clear and simple way. Starting with the basics, it explains core concepts, like Cauchy’s integral formula and power series, using easy language and real-life examples to make the ideas more relatable. Ideal for students or anyone curious about complex analysis, this audiobook aims to build a solid understanding without overwhelming you with complicated terms or symbols, making it perfect for learning on the go. Duration - 12h 57m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:00:59
Introduction to Complex Numbers
Duration:00:01:19
Historical Background
Duration:00:09:04
Definition and Properties of Complex Numbers
Duration:00:08:51
The Complex Plane and Argand Diagram
Duration:00:08:52
Polar and Exponential Forms
Duration:00:07:45
Operations with Complex Numbers
Duration:00:08:13
Roots of Complex Numbers
Duration:00:07:19
Complex Conjugates
Duration:00:07:19
Complex Functions and Mappings
Duration:00:01:15
Definition of Complex Functions
Duration:00:07:13
Complex Mappings and Transformations
Duration:00:07:36
Limits of Complex Functions
Duration:00:08:02
Continuity of Complex Functions
Duration:00:07:37
Elementary Complex Functions
Duration:00:09:01
Complex Powers and Logarithms
Duration:00:04:32
Special Mappings in Complex Analysis
Duration:00:08:53
Limits and Continuity in Complex Analysis
Duration:00:01:24
The Concept of Limits in the Complex Plane
Duration:00:08:06
Properties of Complex Limits
Duration:00:08:03
Uniform and Pointwise Convergence
Duration:00:08:04
Epsilon-Delta Definition for Complex Functions
Duration:00:08:59
Sequential Continuity
Duration:00:08:22
Examples and Problems in Limits and Continuity
Duration:00:08:03
Differentiation in the Complex Plane
Duration:00:01:15
Definition of Complex Derivatives
Duration:00:06:30
Rules of Differentiation for Complex Functions
Duration:00:07:20
Geometric Interpretation of Differentiation
Duration:00:07:15
Differentiability and Analyticity
Duration:00:07:31
The Power Rule and Higher Order Derivatives
Duration:00:06:44
Harmonic Conjugates
Duration:00:06:51
Applications of Complex Differentiation
Duration:00:07:36
Cauchy-Riemann Equations and Analyticity
Duration:00:01:10
Deriving the Cauchy-Riemann Equations
Duration:00:06:51
Implications of the Cauchy-Riemann Equations
Duration:00:06:36
Analytic Functions and Their Properties
Duration:00:06:34
Harmonic Functions and Their Relationship to Analyticity
Duration:00:07:34
Applications of Cauchy-Riemann Equations
Duration:00:09:31
Examples of Analytic and Non-Analytic Functions
Duration:00:07:41
Singularities in Analytic Functions
Duration:00:07:45
Complex Integration
Duration:00:01:13
Introduction to Complex Integration
Duration:00:07:27
Line Integrals in the Complex Plane
Duration:00:07:27
Parametrization of Paths
Duration:00:07:08
Properties of Complex Integrals
Duration:00:07:36
Fundamental Theorem of Complex Integration
Duration:00:07:11
Examples and Computation of Line Integrals
Duration:00:08:31
Path Independence and Connected Domains
Duration:00:06:44
Cauchy’s Theorem and Applications
Duration:00:01:17
Statement and Proof of Cauchy’s Theorem
Duration:00:06:40
Applications of Cauchy’s Theorem
Duration:00:06:32
Deformation of Contours
Duration:00:06:36
Simple and Multiply Connected Domains
Duration:00:05:59
Cauchy-Goursat Theorem
Duration:00:04:57
Morera’s Theorem
Duration:00:04:55
Consequences of Cauchy’s Theorem
Duration:00:05:58
Cauchy’s Integral Formula
Duration:00:01:20
Statement of Cauchy’s Integral Formula
Duration:00:04:23
Applications of the Integral Formula
Duration:00:07:47
Extensions and Corollaries
Duration:00:09:19
Higher Order Derivatives
Duration:00:09:03
Integral Formula for Derivatives
Duration:00:08:03
Proofs and Examples
Duration:00:07:18
Implications of Cauchy’s Integral Formula
Duration:00:07:39
Series Representations of Analytic Functions
Duration:00:01:28
Power Series in Complex Analysis
Duration:00:08:06
Convergence of Power Series
Duration:00:07:47
Taylor Series for Complex Functions
Duration:00:05:14
Laurent Series
Duration:00:06:00
Examples of Series Expansions
Duration:00:07:00
Analytic Continuation
Duration:00:07:14
Applications of Series Representations
Duration:00:06:54
Residues and Poles
Duration:00:01:26
Isolated Singularities
Duration:00:07:17
Classification of Singularities
Duration:00:07:09
Residues and Their Computation
Duration:00:07:02
Poles and Essential Singularities
Duration:00:06:38
Residue at Infinity
Duration:00:06:48
Examples and Applications of Residues
Duration:00:06:26
Series Expansions and Residues
Duration:00:07:18
The Residue Theorem and Applications
Duration:00:01:21
Statement of the Residue Theorem
Duration:00:06:34
Proof and Examples of the Residue Theorem
Duration:00:07:21
Applications in Complex Integration
Duration:00:07:22
Computing Real Integrals with Residues
Duration:00:08:12
Residues and Improper Integrals
Duration:00:07:52
Integral Representations of Special Functions
Duration:00:06:56
Advanced Applications of the Residue Theorem
Duration:00:06:53
Conformal Mappings
Duration:00:01:17
Definition and Properties of Conformal Maps
Duration:00:06:34
Examples of Conformal Mappings
Duration:00:06:44
Riemann Mapping Theorem
Duration:00:06:11
Applications in Physics and Engineering
Duration:00:06:16
Mobius Transformations
Duration:00:05:39
Bilinear Transformations
Duration:00:06:27
Conformal Mapping Techniques
Duration:00:06:22
Harmonic Functions and the Laplace Equation
Duration:00:01:26
Definition of Harmonic Functions
Duration:00:06:32
Laplace’s Equation in Complex Analysis
Duration:00:06:52
Harmonic Conjugates and Analyticity
Duration:00:06:11
The Mean Value Property
Duration:00:05:20
Maximum Principle for Harmonic Functions
Duration:00:05:12
Poisson’s Integral Formula
Duration:00:05:49
Applications of Harmonic Functions
Duration:00:06:53
Fluid Flow and Complex Potentials
Duration:00:06:15
Electrostatics and Complex Analysis
Duration:00:07:06
Heat Conduction Problems
Duration:00:06:37
Applications in Mechanical Engineering
Duration:00:07:15
Applications in Signal Processing
Duration:00:08:10
Complex Analysis in Control Theory
Duration:00:08:07
Miscellaneous Applications
Duration:00:09:22
Advanced Topics in Complex Analysis
Duration:00:01:25
Riemann Surfaces
Duration:00:06:41
Analytic Continuation and Monodromy
Duration:00:06:20
Elliptic Functions
Duration:00:06:29
Hypergeometric Functions
Duration:00:07:17
Complex Dynamics and Fractals
Duration:00:07:59
Modular Forms and Applications
Duration:00:07:15
Current Research and Open Problems
Duration:00:08:09