The programmed approach, established in the first two editions is maintained in the third and it provides a sound foundation from which the student can build a solid engineering understanding. This edition has been modified to reflect the changes in the syllabuses which students encounter before beginning undergraduate studies. The first two chapters include material that assumes the reader has little previous experience in maths. Written by CHarles Evans who lectures at the University of Portsmouth and has been teaching engineering and applied mathematics for more than 25 years. This text provides one of the essential tools for both undergraduate students and professional engineers.

C. Evans

Preface
Acknowledgements
To the Student
1 Basic Ideas
Arithmetic
Representation
Decimal places and significant figures
Precedence
Set notation
Deductions
Algebra
Rules of elementary algebra
Workshop
Identities and equations
Simultaneous equations
Rational expressions
Rearranging equations
Quadratic equations
Polynomials
The binomial theorem
Workshop
The general binomial theorem
Practical
Summary
Assignment
Further exercises
Further concepts
Indices and logarithms
Inequalities
Rules for inequalities
Partial fractions
Workshop
Set notation
Functions
Methods of proof
Practical
Summary
Exercises
Assignment
Further exercises
Trigonometry and geometry
Coordinate systems
Circular functions
Trigonometrical identities
The form a cos 0 + b sin 0
Solutions of equations
Workshop
Coordinate geometry
The straight line
The circle
The conic sections
Workshop
Practical
Summary
Exercises
Assignment
Further exercises
Limits, continuity and differentiation
Limits
The laws of limits
Workshop
Right and left limits
Continuity
Differentiability
Leibniz's theorem
Techniques of differentiation
Workshop
Logarithmic differentiation
Implicit differentiation
Parametric differentiation
Rates of change
Workshop
Practical
Summary
Exercises
Assignments
Further exercises
Hyperbolic functions
Definitions and identities
Differentiation of hyperbolic functions
Curve sketching
Workshop
Injective functions
Surjective functions
Bijective functions
Pseudo-inverse functions
Differentiation of inverse functions
The inverse circular functions
Workshop
The inverse hypervolic functions
Practical
Summary
Exercises
Assignment
Further exercises
Further differentiation
Tangents and