COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.
A Course of Mathematics for Engineerings and Scientists - 1st Edition - ISBN: 9780080093772, 9781483154800

A Course of Mathematics for Engineerings and Scientists

1st Edition

Volume 4

Authors: Brian H. Chirgwin Charles Plumpton
eBook ISBN: 9781483154800
Imprint: Pergamon
Published Date: 1st January 1964
Page Count: 362
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


A Course of Mathematics for Engineers and Scientists offers a mathematics course for undergraduate students reading science and engineering at British and Commonwealth Universities and colleges. The aim of this volume is to generalize and develop the ideas and methods of earlier volumes so that the student can appreciate and use the mathematical methods required in the more advanced parts of physics and engineering. This book begins with elementary ideas of vector algebra which are generalized and developed in two ways. The first is an account of vector analysis and the differential and integral operations and theorems concerning vectors. These ideas find their first generalization in tensor analysis and the transformation of coordinates, including orthogonal curvilinear coordinates. The second development is to matrices, where the properties of arrays of elements, linear equations, and quadratic forms are shown to be the generalizations of elementary algebra and, using 'vector space', of familiar geometrical ideas to n dimensions. The solution of differential equations by series provides a general method for the solution of ordinary and some partial differential equations.
A discussion of the properties of the solutions in the light of the Sturm-Liouville theory introduces the conceptions of eigenvalues and orthogonal functions, forming a link with matrices. A chapter on the special functions gives some of the better known properties of Bessel, Legendre, Laguerre, and Hermite functions, which commonly occur in the solution of boundary and initial value problems.

Table of Contents


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 Equation of Field Lines and Level Surfaces


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


Answers to the Exercises



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

About the Authors

Brian H. Chirgwin

Charles Plumpton

Ratings and Reviews