Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets.
Mathematics for Physicists features:
- Interfaces with modern school mathematics syllabuses
- All topics usually taught in the first two years of a physics degree
- Worked examples throughout
- Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website
This text will be an excellent resource for undergraduate students in physics and a quick reference guide for more advanced students, as well as being appropriate for students in other physical sciences, such as astronomy, chemistry and earth sciences.
Slight criticism: only odd numbered questions I each exercise have answers - should be all the questions in this day and age, and there should be full solutions to at least three questions per exercise set, i.e. setting out how to approach a trivial starter question, a main gubbins question and finally a Sunday roast question with trimmings.. At the moment only worked examples have solutions set out, and at times these can be truncated and terse.
This book is in keeping with the genuinely high standards expected of a Wiley science text, with 565 pages well bound into a paperback format, clear layout, ample use of sub-headings, formulae, graphs, charts and block colour. The rear of the book has answers to selected problems that are included in the text and a comprehensive subject index. The book starts with an in-depth contents sections which tells you exactly where you can find each change of subject.
It is also worth noting that this book is part of the Manchester Physics Series.
The book covers real numbers, variables and functions, including algebraic and trigonometric functions, logarithms and exponentials, differential and integral calculus, series, complex numbers, partial differentiation, vectors, determinants, matrices, eigenvalues. eigenvectors, line and multiple integrals, vector calculus, Fourier analysis, ordinary differential equations, series solutions of differential equations and partial differential equations.
Bearing in mind that this book is written to be understandable to people entering their first degree in physics (i.e. just having completed A Level), it is thoughtfully and purposefully presented in a straightforward manner which will benefit all students. It is worth the reminder that unless you are happy to be working at the level of mathematics detailed in this book, physics is not the subject for you!
A very respectable text which all new physics students will benefit from and one possibly to start reading in the holidays before going up to uni for the first time.
I like the approach a lot, and the authors are careful to put each mathematical concept in a physical context... so, why would you want to know about circular integrals? Well, flux through a closed surface... etc. I don't think I found any area that was just left as a dry abstraction.
I appreciate that the popularity of this book will depend a lot upon whether course tutors recommend it, but (as a physics graduate of, er, many years ago) I would wholeheartedly recommend it as a course companion. It's likely to remain on your desk for many years after that as well, as a reference book.