Preface
This 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’.
Structure of the book
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.
Global changes in this edition
- An overall reorganization has been carried out to link the text and examples more
closely to the exercises at the end of each chapter. The symbol 0 has been placed at
appropriate places within the body of the text as a pointer to the relevant exercises.
New examples and exercises have been inserted to give a more complete coverage
of the development of the mathematics.
- In addition to the solutions to the numerical exercises given at the back of the
book, a full set of worked solutions of the end-of-chapter exercises has been placed
on the book’s companion website at http://www.oxfordtextbooks.co.uk/orc/steiner2e
- The opportunity has been taken to consolidate the several major and many minor
corrections and improvements that have been made over the years since publication
of the first edition in 1996. A small number of new historical footnotes have been