Ship-Ship-Hooray! Free Shipping on $25+ Details >

by Jerrold E. Marsden and Michael J. Hoffman

Edition: 3RD 99Copyright: 1999

Publisher: W.H. Freeman

Published: 1999

International: No

This title is currently not available in digital format.

Well, that's no good. Unfortunately, this edition is currently out of stock. Please check back soon.

Available in the Marketplace starting at $29.49

Price | Condition | Seller | Comments |
---|

- Generous in the number of examples, exercises, and applications provided
- Applications include electric potentials, heat conduction, and hydrodynamics-studied with the aid of harmonic functions, conformal mappings, Laplace transforms, asymptotic expansions, and Gamma and Bessel functions
- Intuitive approach enables application-oriented students to skip the more technical parts without sacrificing an understanding of the main theoretical points
- Highly readable text motivates students and encourages self-study

**Preface**

Introduction to Complex Numbers

Properties of Complex Numbers

Some Elementary Functions

Continuous Functions

Analytic Functions

Differentiation of the Elementary Functions

Review Exercises for Chapter 1

Contour Integrals

Supplement: Riemann Sums

Cauchy's Theorem: Intuitive Version

Cauchy's Theorem: Precise Version

Supplement A: Integrals Along

Continuous Curves

Supplement B: Relationship of Cauchy's Theorem to the Jordan Curve Theorem

Cauchy's Integral Formula

Maximum Modulus Theorem and Harmonic Function

Review Exercises for Chapter 2

Convergent Series of Analytic Functions

Power Series and Taylor's Theorem

Laurent's Series and Classification of Singularities

Review Exercises for Chapter 3

Calculation of Residues

The Residue Theorem

Evaluation of Definite Integrals

Evaluation of Infinite Series and

Partial-Fraction Expansions

Review Exercises for Chapter 4

Basic Theory of Conformal Mappings

Fractional Linear and Schwarz-Christoffel Transformations

Applications of Conformal Mapping to Laplace's Equation, Heat

Conduction, Electrostatics, and Hydrodynamics

Review Exercises for Chapter 5

Analytic Continuation and Elementary Riemann Surfaces

Rouché's Theorem and the Principle of the Argument

Mapping Properties of Analytic

Functions

Supplement A: Normal Families and The Riemann Mapping Theorem

Supplement B: The Dynamics of Complex Analytic Mappings

Review Exercises for Chapter 6

Infinite Products and the Gamma Function

Asymptotic Expansions and the Method of Steepest Descent

Supplement: Bounded Variation and the Proof of the Stationary Phase Formula

Stirling's Formula and Bessel

Functions

Review Exercises for Chapter 7

Basic Properties of LaPlace Transforms

The Complex Inversion Formula

Application of Laplace Transforms to Ordinary Differential Equations

Supplement: The Fourier Transform and the Wave Equation

Review Exercises for Chapter 8

**Index**

shop us with confidence

Summary

- Generous in the number of examples, exercises, and applications provided
- Applications include electric potentials, heat conduction, and hydrodynamics-studied with the aid of harmonic functions, conformal mappings, Laplace transforms, asymptotic expansions, and Gamma and Bessel functions
- Intuitive approach enables application-oriented students to skip the more technical parts without sacrificing an understanding of the main theoretical points
- Highly readable text motivates students and encourages self-study

Table of Contents
#### 1. Analytic Functions

#### 2. Cauchy's Theorem

#### 3. Series Representation of Analytic Functions

#### 4. Calculus of Residues

#### 5. Conformal Mappings

#### 6. Further Development of the Theory

#### 7. Asymptotic Methods

#### 8. The Laplace Transform and Applications

**Preface**

Introduction to Complex Numbers

Properties of Complex Numbers

Some Elementary Functions

Continuous Functions

Analytic Functions

Differentiation of the Elementary Functions

Review Exercises for Chapter 1

Contour Integrals

Supplement: Riemann Sums

Cauchy's Theorem: Intuitive Version

Cauchy's Theorem: Precise Version

Supplement A: Integrals Along

Continuous Curves

Supplement B: Relationship of Cauchy's Theorem to the Jordan Curve Theorem

Cauchy's Integral Formula

Maximum Modulus Theorem and Harmonic Function

Review Exercises for Chapter 2

Convergent Series of Analytic Functions

Power Series and Taylor's Theorem

Laurent's Series and Classification of Singularities

Review Exercises for Chapter 3

Calculation of Residues

The Residue Theorem

Evaluation of Definite Integrals

Evaluation of Infinite Series and

Partial-Fraction Expansions

Review Exercises for Chapter 4

Basic Theory of Conformal Mappings

Fractional Linear and Schwarz-Christoffel Transformations

Applications of Conformal Mapping to Laplace's Equation, Heat

Conduction, Electrostatics, and Hydrodynamics

Review Exercises for Chapter 5

Analytic Continuation and Elementary Riemann Surfaces

Rouché's Theorem and the Principle of the Argument

Mapping Properties of Analytic

Functions

Supplement A: Normal Families and The Riemann Mapping Theorem

Supplement B: The Dynamics of Complex Analytic Mappings

Review Exercises for Chapter 6

Infinite Products and the Gamma Function

Asymptotic Expansions and the Method of Steepest Descent

Supplement: Bounded Variation and the Proof of the Stationary Phase Formula

Stirling's Formula and Bessel

Functions

Review Exercises for Chapter 7

Basic Properties of LaPlace Transforms

The Complex Inversion Formula

Application of Laplace Transforms to Ordinary Differential Equations

Supplement: The Fourier Transform and the Wave Equation

Review Exercises for Chapter 8

**Index**

Publisher Info

Publisher: W.H. Freeman

Published: 1999

International: No

Published: 1999

International: No

- Generous in the number of examples, exercises, and applications provided
- Applications include electric potentials, heat conduction, and hydrodynamics-studied with the aid of harmonic functions, conformal mappings, Laplace transforms, asymptotic expansions, and Gamma and Bessel functions
- Intuitive approach enables application-oriented students to skip the more technical parts without sacrificing an understanding of the main theoretical points
- Highly readable text motivates students and encourages self-study

**Preface**

Introduction to Complex Numbers

Properties of Complex Numbers

Some Elementary Functions

Continuous Functions

Analytic Functions

Differentiation of the Elementary Functions

Review Exercises for Chapter 1

Contour Integrals

Supplement: Riemann Sums

Cauchy's Theorem: Intuitive Version

Cauchy's Theorem: Precise Version

Supplement A: Integrals Along

Continuous Curves

Supplement B: Relationship of Cauchy's Theorem to the Jordan Curve Theorem

Cauchy's Integral Formula

Maximum Modulus Theorem and Harmonic Function

Review Exercises for Chapter 2

Convergent Series of Analytic Functions

Power Series and Taylor's Theorem

Laurent's Series and Classification of Singularities

Review Exercises for Chapter 3

Calculation of Residues

The Residue Theorem

Evaluation of Definite Integrals

Evaluation of Infinite Series and

Partial-Fraction Expansions

Review Exercises for Chapter 4

Basic Theory of Conformal Mappings

Fractional Linear and Schwarz-Christoffel Transformations

Applications of Conformal Mapping to Laplace's Equation, Heat

Conduction, Electrostatics, and Hydrodynamics

Review Exercises for Chapter 5

Analytic Continuation and Elementary Riemann Surfaces

Rouché's Theorem and the Principle of the Argument

Mapping Properties of Analytic

Functions

Supplement A: Normal Families and The Riemann Mapping Theorem

Supplement B: The Dynamics of Complex Analytic Mappings

Review Exercises for Chapter 6

Infinite Products and the Gamma Function

Asymptotic Expansions and the Method of Steepest Descent

Supplement: Bounded Variation and the Proof of the Stationary Phase Formula

Stirling's Formula and Bessel

Functions

Review Exercises for Chapter 7

Basic Properties of LaPlace Transforms

The Complex Inversion Formula

Application of Laplace Transforms to Ordinary Differential Equations

Supplement: The Fourier Transform and the Wave Equation

Review Exercises for Chapter 8

**Index**