vi Preface
added to accompany new material. The material within some chapters has been
reordered to make the development of the subject more logical.
Other principal changes
Chapter 1. A new section, Factorization, factors, and factorials, fills a gap in the coverage
of elementary topics. The rules of precedence for arithmetic operationshas been
brought forward from chapter 2 and extended with examples and exercises,
providing further revision and practice of the arithmetic that is so important for
the understanding of the material in subsequent chapters. The biggest change in
the chapter, reflected in the change of title to Numbers, variables, and units, is a
rewritten and much enlarged section on units to make it a more authoritative and
useful account of this important but often neglected topic. It includes new examples
of the type met in the physical sciences, a brief subsection on dimensional analysis,
and a new example and exercise on the structure of atomic units.
Chapter 2. Parts of the chapter have been rewritten to accommodate more discussion
of the factorization and manipulation of algebraic expressions.
Chapter 7. Numerous small changes have been made, including an introduction to
the multinomial expansion, and revision of the discussion of the Taylor series.
Chapter 9. Section 9.8 has been rewritten to clarify the relevance of line integrals to
change of state in thermodynamics.
Chapter 13. The section on the Frobenius method has been revised, with new and
more demanding examples and exercises.
Chapter 19. Sections 19.2 and 19.3 on eigenvalues and eigenvectors have been
rewritten, with new examples and exercises, to improve the flow and clarity of the
discussion.
Acknowledgements
I wish to express my gratitude to colleagues and students at Exeter University and other
institutions for their often helpful comments on the previous edition of the book, for
pointing out errors and obscurities, and for their suggestions for improvements. I
particularly want to thank Anthony Legon for his valuable comments on the revised
chapters 1 and 9.
I also wish to thank the reviewers of this book for their generous response to the
proposal of a second edition, and the staff of Oxford University Press for their
patience and help.
Above all, I want to thank my wife Mary, without whom nothing could have been
done.
Erich Steiner, Exeter, June 2007