This is one of the books in a series designed to provide engineering students in colleges and universities with a mathematical toolkit. In the United Kingdom it is aimed primarily at HNC/HND students and first-year undergraduates. Thus the mathematics assumed is that in BTEC National Certificates and Diplomas the GNVQ Advanced level or in A level. The pace of development of the mathematics has been aimed at the notional reader for whom mathematics is not their prime interest or "best subject" but need the mathematics in their other studies. The mathematics is developed and applied in an engineering context with large numbers of worked examples and problems, all with answers being supplied. This book is concerned with the principles of differentiation and integration. A familarity with basic algebra and a basic knowledge of common functions, such as polynomials, trigonometric, exponential, logarithmic and hyperbolic, is assumed. An appendix giving supportive mathematics on these functions is included. The aim of the book has been to include sufficient worked examples and problems to enable the reader to acquire some understanding and proficiency in the use of differentiation and integration to solve engineering problems.