A Course of Mathematics for Engineerings and Scientists

A Course of Mathematics for Engineerings and Scientists

Volume 5

1st Edition - January 1, 1964

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  • Authors: Brian H. Chirgwin, Charles Plumpton
  • eBook ISBN: 9781483160795

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Description

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.

Table of Contents


  • 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


Product details

  • No. of pages: 210
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483160795

About the Authors

Brian H. Chirgwin

Charles Plumpton

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