Complex Analysis

A textbook for an introductory course in complex analysis. Topics from complex function theory, including contour integration and conformal mapping.

**Tag(s):**
Mathematics

**Publication date**:

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
107 pages

**Views**: 21,664

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 11 Jan 2007 06:33:32

Complex Analysis

A textbook for an introductory course in complex analysis. Topics from complex function theory, including contour integration and conformal mapping.

Book Excerpts:

This is a textbook for an introductory course in complex analysis. It has been used for undergraduate complex analysis course at Georgia Institute of Technology.

This course is destined to introduce the student to the basic results in complex variable theory, in particular Cauchy's theorem, and to develop the student's facility in the following three areas:

- Computing the Laurent or Taylor series expansions associated to a function which is analytic in part of the complex plane, and the determination of the region of convergence of such series

- Computing definite integrals by means of the residue calculus

- Solving boundary value problems associated to the Laplace operator by means of the conformal transformations associated to analytic functions

Topics to be covered:

- Geometry of the complex plane, triangle inequalities, geometric proof of the fundamental theorem of algebra

- Analytic functions: Continuity and differentiability, the Cauchy-Riemann equations. Complex functions as maps of the complex plane into itself

- Elementary analytic functions, including the logarithm, and its principle branch, log(z)

- Line integrals, the Cauchy integral formula and the Cauchy-Goursat theorem (proof of the Cauchy formula to be based on Green's theorem), Morera's theorem, etc.

- Series: Taylor and Laurent expansions

- Residue calculus for definite integrals

- Harmonic functions and analytic functions: conjugate harmonics, conformal invariance of break Laplace's equation in the plane, the Cauchy-Riemann equations and conformal maps

- Poisson kernel derived from Cauchy's formula; solution of boundary value problems for Laplace's equation by conformal mapping, selected applications

This is a textbook for an introductory course in complex analysis. It has been used for undergraduate complex analysis course at Georgia Institute of Technology.

This course is destined to introduce the student to the basic results in complex variable theory, in particular Cauchy's theorem, and to develop the student's facility in the following three areas:

- Computing the Laurent or Taylor series expansions associated to a function which is analytic in part of the complex plane, and the determination of the region of convergence of such series

- Computing definite integrals by means of the residue calculus

- Solving boundary value problems associated to the Laplace operator by means of the conformal transformations associated to analytic functions

Topics to be covered:

- Geometry of the complex plane, triangle inequalities, geometric proof of the fundamental theorem of algebra

- Analytic functions: Continuity and differentiability, the Cauchy-Riemann equations. Complex functions as maps of the complex plane into itself

- Elementary analytic functions, including the logarithm, and its principle branch, log(z)

- Line integrals, the Cauchy integral formula and the Cauchy-Goursat theorem (proof of the Cauchy formula to be based on Green's theorem), Morera's theorem, etc.

- Series: Taylor and Laurent expansions

- Residue calculus for definite integrals

- Harmonic functions and analytic functions: conjugate harmonics, conformal invariance of break Laplace's equation in the plane, the Cauchy-Riemann equations and conformal maps

- Poisson kernel derived from Cauchy's formula; solution of boundary value problems for Laplace's equation by conformal mapping, selected applications

Tweet

About The Author(s)

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors