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1 Burnside - Bldg. 2 Mathematics- Complex Analysis

Applied Complex Variables (Mathematics Series)

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Applied Complex Variables (Mathematics Series) Cover

 

Synopses & Reviews

Publisher Comments:

Analytic function theory is a traditional subject going back to Cauchy and Riemann in the 19th century. Once the exclusive province of advanced mathematics students, its applications have proven vital to today's physicists and engineers. In this highly regarded work, Professor John W. Dettman offers a clear, well-organized overview of the subject and various applications — making the often-perplexing study of analytic functions of complex variables more accessible to a wider audience.
The first half of Applied Complex Variables, designed for sequential study, is a step-by-step treatment of fundamentals, presenting superior coverage of concepts of complex analysis, including the complex number plane; functions and limits; the Cauchy-Riemann conditions for differentiability; Riemann surfaces; the definite integral; power series; meromorphic functions; and much more. The second half provides lucid exposition of five important applications of analytic function theory, each approachable independently of the others: potential theory; ordinary differential equations; Fourier transforms; Laplace transforms; and asymptotic expansions. Helpful exercises are included at the end of each topic in every chapter.

The two-part structure of Applied Complex Variables affords the college instructor maximum classroom flexibility. Once fundamentals are mastered, applications can be studied in any sequence desired. Depending on how many are selected for study, Professor Dettman's impressive text is ideal for either a one- or two-semester course. And, of course, the ambitious student possessing a knowledge of basic calculus will find its straightforward approach rewarding to his independent study efforts.

Applied Complex Variables is a cogent, well-written introduction to an important and exciting branch of advanced mathematics — serving both the theoretical needs of the mathematics specialist and the applied math needs of the physicist and engineer. Students and teachers alike will welcome this timely, moderately priced reissue of a widely respected work.

Synopsis:

Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Synopsis:

Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, asymptotic expansions. Includes 66 figures and features exercises at end of each chapter.

Synopsis:

First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half deals with potential theory; ordinary differential equations; Fourier transforms; Laplace transforms and asymptotic expansion. Exercises included.

Table of Contents

Part I. Analytic Function Theory

Chapter 1. The Complex Number Plane

  1.1 Introduction

  1.2 Complex Numbers

  1.3 The Complex Plane

  1.4 Point Sets in the Plane

  1.5 Stereographic Projection. The Extended Complex Plane

  1.6 Curves and Regions

Chapter 2. Functions of a Complex Variable

  2.1 Functions and Limits

  2.2 Differentiability and Analyticity

  2.3 The Cauchy-Riemann Conditions

  2.4 Linear Fractional Transformations

  2.5 Transcendental functions

  2.6 Riemann Surfaces

Chapter 3. Integration in the Complex Plane

  3.1 Line Integrals

  3.2 The Definite Integral

  3.3 Cauchy's Theorem

  3.4 Implications of Cauchy's Theorem

  3.5 Functions Defined by Integration

  3.6 Cauchy Formulas

  3.7 Maximum Modulus Principle

Chapter 4. Sequences and Series

  4.1 Sequences of Complex Numbers

  4.2 Sequences of Complex Functions

  4.3 Infinite Series

  4.4 Power Series

  4.5 Analytic Continuation

  4.6 Laurent Series

  4.7 Double Series

  4.8 Infinite Products

  4.9 Improper Integrals

  4.10 The Gamma Function

Chapter 5. Residue Calculus

  5.1 The Residue Theorem

  5.2 Evaluation of Real Integrals

  5.3 The Principle of the Argument

  5.4 Meromorphic Functions

  5.5 Entire Functions

Part II. Applications of Analytic Function Theory

Chapter 6. Potential Theory

  6.1 Laplace's Equation in Physics

  6.2 The Dirichlet Problem

  6.3 Green's Functions

  6.4 Conformal Mapping

  6.5 The Schwarz-Christoffel Transformation

  6.6 Flows with Sources and Sinks

  6.7 Volume and Surface Distributions

  6.8 Singular Integral Equations

Chapter 7. Ordinary Differential Equations

  7.1 Separation of Variables

  7.2 Existence and Uniqueness Theorems

  7.3 Solution of a Linear Second-Order Differential Equation Near an Ordinary Point

  7.4 Solution of a Linear Second-Order Differential Equation Near a Regular Singular Point

  7.5 Bessel Functions

  7.6 Legendre Functions

  7.7 Sturm-Liouville Problems

  7.8 Fredholm Integral Equations

Chapter 8. Fourier Transforms

  8.1 Fourier Series

  8.2 The Fourier Integral Theorem

  8.3 The Complex Fourier Transform

  8.4 Properties of the Fourier Transform

  8.5 The Solution of Ordinary Differential Equations

  8.6 The Solution of Partial Differential Equations

  8.7 The Solution of Integral Equations

Chapter 9. Laplace Transforms

  9.1 From Fourier to Laplace Transform

  9.2 Properties of the Laplace Transform

  9.3 Inversion of Laplace Transforms

  9.4 The Solution of Ordinary Differential Equations

  9.5 Stability

  9.6 The Solution of Partial Differential Equations

  9.7 The Solution of Integral Equations

Chapter 10. Asymptotic Expansions

  10.1 Introduction and Definitions

  10.2 Operations on Asymptotic Expansions

  10.3 Asymptotic Expansion of Integrals

  10.4 Asymptotic Solutions of Ordinary Differential Equations

  References; Index

Product Details

ISBN:
9780486646701
Author:
Dettman, John W.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Dettman, John W.
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Calculus
Subject:
Advanced
Subject:
Functions of complex variables
Subject:
General Mathematics
Subject:
Functional Analysis
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
v. 5
Publication Date:
20100631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
512
Dimensions:
8.5 x 5.38 in 1.19 lb

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Related Subjects


Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Complex Analysis
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Applied Complex Variables (Mathematics Series) Used Trade Paper
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Product details 512 pages Dover Publications - English 9780486646701 Reviews:
"Synopsis" by ,
Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.
"Synopsis" by , Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, asymptotic expansions. Includes 66 figures and features exercises at end of each chapter.
"Synopsis" by ,
First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half deals with potential theory; ordinary differential equations; Fourier transforms; Laplace transforms and asymptotic expansion. Exercises included.
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