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Cover type: Hardback

Edition: 98

Copyright: 1998

Publisher: CRC Press I, LLC

Published: 1998

International: No

Edition: 98

Copyright: 1998

Publisher: CRC Press I, LLC

Published: 1998

International: No

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This text/reference covers essential areas of engineering mathematics involving single, multiple, and complex variations. Taken as a whole, this book provides a succinct, carefully organized guide for mastering engineering mathematics.

Unlike typical textbooks, *Advanced Engineering Mathematics *begins with a thorough exploration of complex variables because they provide powerful techniques for understanding topics, such as Fourier, Laplace and z-transforms, introduced later in the text. The book contains a wealth of examples, both classic problems used to illustrate concepts, and interesting real-life examples from scientific literature.

Ideal for a two-semester course on advanced engineering mathematics, *Advanced Engineering Mathematics* is concise and well-organized, unlike the long, detailed texts used to teach this subject. Since almost every engineer and many scientists need the skills covered in this book for their daily work, *Advanced Engineering Mathematics *also makes an excellent reference for practicing engineers and scientists.

Covers advanced engineering mathematics topics involving single, multiple, and complex variables

Covers the latest topics such as the Z-transform

Contains a wealth of examples, as well as classical problems from the scientific and engineering literature

Includes an instructor's manual with solutions to all problems

Includes many historical notes to provide a perspective on engineering mathematics

Provides computational projects for the chapters on Fourier Analysis, Numerical Solutions of Partial Differential Equations, and Linear Algebra

Begins with a thorough exploration of complex variables used to explain topics introduced later in the text

Introduction

Complex Variables

Complex Numbers

Finding Roots

The Derivative in the Complex Plane: The Cauchy-Riemann Equations

Line Integrals

Cauchy-Goursat Theorem

Cauchy's Integral Formula

Taylor and Laurent Expansions and Singularities

Theory of Residues

Evaluation of Real Definite Integrals

Fourier Series

Fourier Series

Properties of Fourier Series

Half-Range Expansions

Fourier Series with Phase Angles

Complex Fourier Series

The Use of Fourier Series in the Solution of Ordinary Differential Equations

Finite Fourier Series

The Fourier Transform

Fourier Transform

Fourier Transforms Containing the Delta Function

Properties of Fourier Transforms

Inversion of Fourier Transforms

Convolution

Solution of Ordinary Differential Equations by Fourier Transforms

The Laplace Transform

Definition and Elementary Properties

Heaviside Step and Dirac Delta Functions

Some Useful Theorems

The Laplace Transform of a Periodic Function

Inversion by Partial Fractions: Heaviside's Expansion Theorem

Convolution

Integral Equations

Solution of Linear Differential Equations with Constant Coefficients

Transfer Functions, Green's Function, and Indicial Admittance

Inversion by Contour Integration

The Z-Transform

The Relationship of the Z-Transform to the Laplace Transform

Some Useful Properties

Inverse Z-Transforms

Solution of Difference Equations

Stability of Discrete-Time Systems

The Sturm-Liouville Problem

Eigenvalues and Eigenfunctions

Orthogonality of Eigenfunctions

Expansion in Series of Eigenfunction

A Singular Sturm-Liouville Problem: Legendre's Equation

Another Singular Sturm-Liouville Problem: Bessel's Equation

The Wave Equation

The Vibrating String

Initial Conditions: Cauchy Problem

Separation of Variables

D'Alembert's Formula

The Laplace Transform Method

Numerical Solution of the Wave Equation

The Heat Equation

Derivation of the Heat Equation

Initial and Boundary Conditions

Separation of Variables

The Laplace Transform Method

The Fourier Transform Method

The Superposition Integral

Numerical Solution of the Heat Equation

Laplace's Equation

Derivation of Laplace's Equation

Boundary Conditions

Separation of Variables

The Solution of Laplace's Equation on the Upper Half-Plane

Poisson's Equation in a Rectangle

The Laplace Transform Method

Numerical Solution of Laplace's Equation

Vector Analysis

Review

Divergence and Curl

Line Integrals

The Potential Function

Surface Integrals

Green's Lemma

Stokes' Theorem

Divergence Theorem

Linear Algebra

Fundamentals of Linear Equations

Determinants

Cramer's Rule

Row Echelon Form and Gaussian Elimination

Eigenvalues and Eigenvectors

Systems of Linear Differential Equations

Answers to the Odd-Numbered Problems

Index

Summary

This text/reference covers essential areas of engineering mathematics involving single, multiple, and complex variations. Taken as a whole, this book provides a succinct, carefully organized guide for mastering engineering mathematics.

Unlike typical textbooks, *Advanced Engineering Mathematics *begins with a thorough exploration of complex variables because they provide powerful techniques for understanding topics, such as Fourier, Laplace and z-transforms, introduced later in the text. The book contains a wealth of examples, both classic problems used to illustrate concepts, and interesting real-life examples from scientific literature.

Ideal for a two-semester course on advanced engineering mathematics, *Advanced Engineering Mathematics* is concise and well-organized, unlike the long, detailed texts used to teach this subject. Since almost every engineer and many scientists need the skills covered in this book for their daily work, *Advanced Engineering Mathematics *also makes an excellent reference for practicing engineers and scientists.

Covers advanced engineering mathematics topics involving single, multiple, and complex variables

Covers the latest topics such as the Z-transform

Contains a wealth of examples, as well as classical problems from the scientific and engineering literature

Includes an instructor's manual with solutions to all problems

Includes many historical notes to provide a perspective on engineering mathematics

Provides computational projects for the chapters on Fourier Analysis, Numerical Solutions of Partial Differential Equations, and Linear Algebra

Begins with a thorough exploration of complex variables used to explain topics introduced later in the text

Table of Contents

Introduction

Complex Variables

Complex Numbers

Finding Roots

The Derivative in the Complex Plane: The Cauchy-Riemann Equations

Line Integrals

Cauchy-Goursat Theorem

Cauchy's Integral Formula

Taylor and Laurent Expansions and Singularities

Theory of Residues

Evaluation of Real Definite Integrals

Fourier Series

Fourier Series

Properties of Fourier Series

Half-Range Expansions

Fourier Series with Phase Angles

Complex Fourier Series

The Use of Fourier Series in the Solution of Ordinary Differential Equations

Finite Fourier Series

The Fourier Transform

Fourier Transform

Fourier Transforms Containing the Delta Function

Properties of Fourier Transforms

Inversion of Fourier Transforms

Convolution

Solution of Ordinary Differential Equations by Fourier Transforms

The Laplace Transform

Definition and Elementary Properties

Heaviside Step and Dirac Delta Functions

Some Useful Theorems

The Laplace Transform of a Periodic Function

Inversion by Partial Fractions: Heaviside's Expansion Theorem

Convolution

Integral Equations

Solution of Linear Differential Equations with Constant Coefficients

Transfer Functions, Green's Function, and Indicial Admittance

Inversion by Contour Integration

The Z-Transform

The Relationship of the Z-Transform to the Laplace Transform

Some Useful Properties

Inverse Z-Transforms

Solution of Difference Equations

Stability of Discrete-Time Systems

The Sturm-Liouville Problem

Eigenvalues and Eigenfunctions

Orthogonality of Eigenfunctions

Expansion in Series of Eigenfunction

A Singular Sturm-Liouville Problem: Legendre's Equation

Another Singular Sturm-Liouville Problem: Bessel's Equation

The Wave Equation

The Vibrating String

Initial Conditions: Cauchy Problem

Separation of Variables

D'Alembert's Formula

The Laplace Transform Method

Numerical Solution of the Wave Equation

The Heat Equation

Derivation of the Heat Equation

Initial and Boundary Conditions

Separation of Variables

The Laplace Transform Method

The Fourier Transform Method

The Superposition Integral

Numerical Solution of the Heat Equation

Laplace's Equation

Derivation of Laplace's Equation

Boundary Conditions

Separation of Variables

The Solution of Laplace's Equation on the Upper Half-Plane

Poisson's Equation in a Rectangle

The Laplace Transform Method

Numerical Solution of Laplace's Equation

Vector Analysis

Review

Divergence and Curl

Line Integrals

The Potential Function

Surface Integrals

Green's Lemma

Stokes' Theorem

Divergence Theorem

Linear Algebra

Fundamentals of Linear Equations

Determinants

Cramer's Rule

Row Echelon Form and Gaussian Elimination

Eigenvalues and Eigenvectors

Systems of Linear Differential Equations

Answers to the Odd-Numbered Problems

Index

Publisher Info

Publisher: CRC Press I, LLC

Published: 1998

International: No

Published: 1998

International: No

Unlike typical textbooks, *Advanced Engineering Mathematics *begins with a thorough exploration of complex variables because they provide powerful techniques for understanding topics, such as Fourier, Laplace and z-transforms, introduced later in the text. The book contains a wealth of examples, both classic problems used to illustrate concepts, and interesting real-life examples from scientific literature.

Ideal for a two-semester course on advanced engineering mathematics, *Advanced Engineering Mathematics* is concise and well-organized, unlike the long, detailed texts used to teach this subject. Since almost every engineer and many scientists need the skills covered in this book for their daily work, *Advanced Engineering Mathematics *also makes an excellent reference for practicing engineers and scientists.

Covers advanced engineering mathematics topics involving single, multiple, and complex variables

Covers the latest topics such as the Z-transform

Contains a wealth of examples, as well as classical problems from the scientific and engineering literature

Includes an instructor's manual with solutions to all problems

Includes many historical notes to provide a perspective on engineering mathematics

Provides computational projects for the chapters on Fourier Analysis, Numerical Solutions of Partial Differential Equations, and Linear Algebra

Begins with a thorough exploration of complex variables used to explain topics introduced later in the text

Complex Variables

Complex Numbers

Finding Roots

The Derivative in the Complex Plane: The Cauchy-Riemann Equations

Line Integrals

Cauchy-Goursat Theorem

Cauchy's Integral Formula

Taylor and Laurent Expansions and Singularities

Theory of Residues

Evaluation of Real Definite Integrals

Fourier Series

Fourier Series

Properties of Fourier Series

Half-Range Expansions

Fourier Series with Phase Angles

Complex Fourier Series

The Use of Fourier Series in the Solution of Ordinary Differential Equations

Finite Fourier Series

The Fourier Transform

Fourier Transform

Fourier Transforms Containing the Delta Function

Properties of Fourier Transforms

Inversion of Fourier Transforms

Convolution

Solution of Ordinary Differential Equations by Fourier Transforms

The Laplace Transform

Definition and Elementary Properties

Heaviside Step and Dirac Delta Functions

Some Useful Theorems

The Laplace Transform of a Periodic Function

Inversion by Partial Fractions: Heaviside's Expansion Theorem

Convolution

Integral Equations

Solution of Linear Differential Equations with Constant Coefficients

Transfer Functions, Green's Function, and Indicial Admittance

Inversion by Contour Integration

The Z-Transform

The Relationship of the Z-Transform to the Laplace Transform

Some Useful Properties

Inverse Z-Transforms

Solution of Difference Equations

Stability of Discrete-Time Systems

The Sturm-Liouville Problem

Eigenvalues and Eigenfunctions

Orthogonality of Eigenfunctions

Expansion in Series of Eigenfunction

A Singular Sturm-Liouville Problem: Legendre's Equation

Another Singular Sturm-Liouville Problem: Bessel's Equation

The Wave Equation

The Vibrating String

Initial Conditions: Cauchy Problem

Separation of Variables

D'Alembert's Formula

The Laplace Transform Method

Numerical Solution of the Wave Equation

The Heat Equation

Derivation of the Heat Equation

Initial and Boundary Conditions

Separation of Variables

The Laplace Transform Method

The Fourier Transform Method

The Superposition Integral

Numerical Solution of the Heat Equation

Laplace's Equation

Derivation of Laplace's Equation

Boundary Conditions

Separation of Variables

The Solution of Laplace's Equation on the Upper Half-Plane

Poisson's Equation in a Rectangle

The Laplace Transform Method

Numerical Solution of Laplace's Equation

Vector Analysis

Review

Divergence and Curl

Line Integrals

The Potential Function

Surface Integrals

Green's Lemma

Stokes' Theorem

Divergence Theorem

Linear Algebra

Fundamentals of Linear Equations

Determinants

Cramer's Rule

Row Echelon Form and Gaussian Elimination

Eigenvalues and Eigenvectors

Systems of Linear Differential Equations

Answers to the Odd-Numbered Problems

Index