Introduction to Physical Mathematics

by P.G. Harper , D. L. Weaire

• ISBN13: 9780521269087
• ISBN10: 0521269083
• Format: Paperback
• Copyright: 1985-04-26
• Publisher: Cambridge University Press

Summary

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.

Table of Contents

Introduction

Errors

Cartesian coordinates

Vectors

The scalar product

The vector product and rotation

Matrices in physics

The transformation of matrices

The matrix eigenvalue equation

Exponential and logarithm functions

Sine and cosine functions

Graph plotting and curve sketching

Differentiation

Approximations

Power series and Taylor's expansion

Partial differentiation

Integration

The differential equation

Solving first-order differential equations

Second-order differential equations

Solving second-order differential equations

The complex exponential

The circuit equation

Harmonics and Fourier series

The diffusion equation

Waves

The rate of change of a vector

The scalar field and gradient operator

The vector field

Line integration

The potential field

Surface and volume integration

Flux and divergence

Circulation and the curl

Conclusion

Miscellaneous exercises

Table of Contents provided by Publisher. All Rights Reserved.