Cockett M.C.R., Doggett G. Maths for Chemists. Vol. 1: Numbers, Functions and Calculus

Royal Society of Chemistry, 2003. — 192 p.
The two volumes of "Maths for Chemists" provide a resource for all undergraduate chemistry students and are particularly focused on the needs of students who may not have studied mathematics beyond GCSE level (or equivalent). The texts are introductory in nature and adopt a sympathetic approach for students who need support and understanding in working with the diverse mathematical tools required in a typical chemistry degree course. The early chapters of the text provide a succinct introduction to the important mathematical skills of algebraic manipulation, trigonometry, numbers, functions, units and the general grammar of maths. Later chapters build on these basic mathematical principles as a foundation for the development of differential and integral calculus. In spite of the introductory nature of this volume, some of the more important mathematical tools required in quantum chemistry are deliberately included, through a gradual introduction to, and development of, the concept of the eigenvalue problemNumbers and Algebra
Real Numbers
Algebra
Functions and Equations: Their Form and Use
Defining Function
Representation of Functions
Some Special Mathematical Functions
EquationsLimits
Mathematical and Chemical Examples
Defining the Limiting ProcessDifferentiation
The Average Rate of Change
The Instantaneous Rate of Change
Higher Order Derivatives
MAXIMA, Minima and Points of Inflection
The Differentiation of Functions of Two or
More VariablesDifferentials
The Effects of Incremental Change
The Differential of a Function of Two or More Variables
The Propagation of ErrorsIntegration
Reversing the Effects of Differentiation
The Definite Integral
The Indefinite Integral
General Strategies for Solving More
Complicated Integrals
The Connection between the Definite and
Idefinite IntegralDifferential Equations
Using the Derivative of a Function to Create a Differential Equation
Some Examples of Differential Equations Arising in Classical and Chemical Contexts
First-order Differential Equations
Second-order Differential EquationsAnswers to Problems
Subject Index