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Preface

Chapter I. Fourier Series

Introduction: Full-Range Series

The Sine Series and the Cosine Series

Fourier Series in a Range of Arbitrary Width

Double Fourier Series

Applications of Fourier Series

Parseval's Theorem

Chapter II. The Laplace Transformation

Definitions - Ordinary Differential Equations

Simultaneous Ordinary Differential Equations with Constant Coefficients

Some Theorems of the Laplace Transformation - Special Functions

Partial Differential Equations

Chapter III. Functions of a Complex Variable

Introduction - Definitions

Differentiation and Integration of Functions of a Complex Variable

Singularities

Conformal Transformations

The Theory of Residues

The Evaluation of Definite Integrals by Contour Integration

Chapter IV. Fourier Integrals and Transformations: The Inversion Integral for the Laplace Transformation

The Fourier Integral

Fourier Transforms

Examples of the Use of Sine and Cosine Transforms in the Solution of Boundary Value Problems in Mathematical Physics

The Laplace Transformation and the Inversion Integral

Applications of the Inversion Integral to Boundary Value Problems

The 'Wave-Packet' in Quantum Mechanics

Note on Definitions

Answers to The Exercises

Bibliography

Index

- 1st Edition - January 1, 1964
- Authors: Brian H. Chirgwin, Charles Plumpton
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 6 0 7 9 - 5

A Course of Mathematics for Engineers and Scientists, Volume 5 presents the solutions of differential equations by obtaining the results in different forms. This book discusses the… Read more

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Immediately download your ebook while waiting for your print delivery. No promo code is needed.

A Course of Mathematics for Engineers and Scientists, Volume 5 presents the solutions of differential equations by obtaining the results in different forms. This book discusses the significant branch of mathematics generalizing the elementary ideas of function, integration, and differentiation. Organized into four chapters, this volume begins with an overview of the use of Fourier series that leads to solutions consisting of infinite series. This text then discusses the fundamental advantage of Laplace and Fourier transformation. Other chapters consider the technique of obtaining the solutions of ordinary, and several partial, differential equations from definite integrals. This book discusses as well the mathematical basis underlying the transformation methods connecting Laplace and Fourier transformations, which is given by the advancement of complex variable theory. The final chapter deals with the series of devices for inverting the transformation functions. This book is a valuable resource for scientists, engineers, mathematicians, and undergraduate students.

Preface

Chapter I. Fourier Series

Introduction: Full-Range Series

The Sine Series and the Cosine Series

Fourier Series in a Range of Arbitrary Width

Double Fourier Series

Applications of Fourier Series

Parseval's Theorem

Chapter II. The Laplace Transformation

Definitions - Ordinary Differential Equations

Simultaneous Ordinary Differential Equations with Constant Coefficients

Some Theorems of the Laplace Transformation - Special Functions

Partial Differential Equations

Chapter III. Functions of a Complex Variable

Introduction - Definitions

Differentiation and Integration of Functions of a Complex Variable

Singularities

Conformal Transformations

The Theory of Residues

The Evaluation of Definite Integrals by Contour Integration

Chapter IV. Fourier Integrals and Transformations: The Inversion Integral for the Laplace Transformation

The Fourier Integral

Fourier Transforms

Examples of the Use of Sine and Cosine Transforms in the Solution of Boundary Value Problems in Mathematical Physics

The Laplace Transformation and the Inversion Integral

Applications of the Inversion Integral to Boundary Value Problems

The 'Wave-Packet' in Quantum Mechanics

Note on Definitions

Answers to The Exercises

Bibliography

Index

- No. of pages: 210
- Language: English
- Edition: 1
- Published: January 1, 1964
- Imprint: Pergamon
- eBook ISBN: 9781483160795

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