Chun Wa Wong
OXFORD UNIVERSITY PRESS 2013, 736 PAGES
PRICE (HARDBACK) £48.99 ISBN 978-0-199-64139-0
This book consists of eight chapters. Some chapters are very detailed and relatively simple to follow; other chapters are much more advanced and terse in their presentation.
A description of the chapters follows.
Chapter 1 – This chapter is a detailed introduction to vectors and vector fields, reaching vector differential operators in curvilinear coordinates.
Chapter 2 – Is very similar to Chapter 1 in level and covers matrices, eigenvalues and into operators and matrix groups.
Chapter 3 – This is the first of the more advanced chapters covering special relativity, spinors of various kinds and tensors.
Chapter 4 – This chapter covers Fourier series, Fourier transforms, Green’s functions and generalised Fourier series, amongst other topics.
Chapter 5 – Introduces differential equations and includes the separation method for partial differential equations.
Chapter 6 – This is an advanced chapter that considers nonlinear equations, chaos, logistic map, solitons and nonlinear superposition of solitons.
Chapter 7 – This chapter introduces the usual orthogonal functions, leading to the Sturm-Liouville equation.
Chapter 8 – Is the final chapter and is another advanced presentation, covering functions of a complex variable, the Cauchy integral theorem, residues, Laurent series and ending with asymptotic expansions.
Overall this is a first to second year undergraduate book that covers an unusual quantity of material. The book contains many problems to assist with understanding the contents. I would recommend this book to all undergraduates with an interest in mathematical physics, mathematics or physics, although some physics students might find the book a struggle.
John Bartlett CMath MIMA
Book review published directly onto IMA website (October 2015)
