A Course of Mathematics for Engineers and Scientists - 1st Edition - ISBN: 9780080264943, 9781483149592

A Course of Mathematics for Engineers and Scientists

1st Edition

Authors: Brian H. Chirgwin Charles Plumpton
eBook ISBN: 9781483149592
Imprint: Pergamon
Published Date: 1st January 1964
Page Count: 362
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Description

A Course of Mathematics for Engineers and Scientists, Volume 4 focuses on mathematical methods required in the more advanced parts of physics and engineering. Organized into five chapters, this book begins by elucidating vector analysis and the differential and integral operations and theorems concerning vectors. Chapter II shows solution of ordinary and some partial differential equations. Chapter III addresses the properties of Bessel, Legendre, Laguerre, and Hermite functions that commonly occur in the solution of boundary and initial value problems. The last two chapters detail the differential equations of field lines and level surfaces, as well as the matrices. This book will be useful to undergraduate students so that they can appreciate and use the mathematical methods required in the more advanced parts of physics and engineering.

Table of Contents


Preface

Chapter I. Vector Analysis

Transformation of coordinates

Scalar fields: gradient

Vector fields

Line and surface integrals

Applications to vector analysis

Green's theorem

Discontinuities; surface derivatives

Uniqueness theorems and Green's function

Variation with time

Orthogonal curvilinear coordinates

Suffix notation and the summation convention

Cartesian tensors

Chapter II. The Solution of Some Differential Equations

Laplace's equation in two and three dimensions

Solution in series of ordinary differential equations

The behavior of the solution of a differential equation

Eigenvalues: Sturm-Liouville systems

Chapter III. Some Special Functions

Bessel functions

Legendre polynomials

Other special functions

Chapter IV. The Differential Equations of Field Lines and Level Surfaces

Introduction

Field lines

Lagrange's partial differential equation

Level surfaces and orthogonal trajectories

Chapter V. Matrices

Introduction and notation

Matrix algebra

The rank of a matrix: singular matrices

The reciprocal of a square matrix

Partitioned matrices

The solution of linear equations

Vector spaces

Eigenvalues and eigenvectors

Quadratic forms

Simultaneous reduction of quadratic forms

Multiple eigenvalues

Hermitian matrices

Bibliography

Answers to the Exercises

Index




Details

No. of pages:
362
Language:
English
Copyright:
© Pergamon 1964
Published:
Imprint:
Pergamon
eBook ISBN:
9781483149592

About the Author

Brian H. Chirgwin

Charles Plumpton