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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.
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
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
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
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
- No. of pages:
- © Pergamon 1964
- 1st January 1964
- eBook ISBN: