Our aim in writing this book is to produce a relatively short volume that covers all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Thus, it differs from most books, which include many advanced topics, such as tensor analysis, group theory, etc., that are not required in a typical physics degree course, except as specialised options. These books are frequently well over a thousand pages long and contain much more material than most undergraduate students need. In addition, they are often not well interfaced with school mathematics and start at a level that is no longer appropriate. Mathematics teaching at schools has changed over the years and students now enter university with a wide variety of mathematical backgrounds.

The early chapters of the book 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. Although written primarily for the needs of physics students, it would also be appropriate for students in other physical sciences, such as astronomy, chemistry, earth science, etc.

We do not try to cover all the more advanced, optional courses taken by some physics students, since these are already well treated in more advanced texts, which, with some degree of overlap, take up where our book leaves off. The exception is statistics. Although this is required by undergraduate physics students, we have not included it because it is usually taught as a separate topic, using one of the excellent specialised texts already available.

The book has been read in its entirety by one of the editors of the Manchester Physics Series, Jeff Forshaw of Manchester University, and we are grateful to him for many helpful suggestions that have improved the presentation.

B.R. Martin

G. Shaw

April 2015