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his book describes the mathematics required for the full range of topics that make up a university degree course in chemistry. It has been designed as a textbook for courses in ‘mathematics for chemists’. The subject is developed in a logical and consistent way with few assumptions made of prior knowledge of mathematics. The material is organized in three largely independent parts: Chapters 1 to 15 on algebra, the calculus, differential equations, and expansions in series; Chapters 16 to 19 on vectors, determinants, and matrices; Chapters 20 and 21 are introductions to the big topics of numerical analysis and statistics.
A feature of the book is the extensive use of examples to illustrate every important concept and method in the text. Some of these examples have also been used to demonstrate applications of the mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter are an essential element of the development of the subject, and have been designed to give the student a working understanding of the material in the text. The text is accompanied by a ‘footnote history’ of mathematics.
Several topics in chemistry are given extended treatments. These include the concept of pressure–volume work in thermodynamics in Chapter 5, periodic systems in Chapter 8, the differential equations of chemical kinetics in Chapter 11, and several applications of the Schrödinger equation in Chapters 12 and 14. In addition, the contents of several chapters are largely dictated by their applications in the physical sciences: Chapter 9, the mathematics of thermodynamics; Chapters 10 and 16, the description of systems and processes in three dimensions.
Chapter 13 (advanced), some important differential equations and special functions in mathematical chemistry and physics; Chapter 15 (advanced), intermolecular forces, wave analysis, and Fourier transform spectroscopy; Chapters 18 and 19, molecular symmetry and symmetry operations, molecular orbital theory, molecular dynamics, and advanced quantum mechanics. Chapter 1. A new section, Factorization, factors, and factorials, fills a gap in the coverage of elementary topics.
The rules of precedence for arithmetic operations has 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. 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.