Overview

Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering:

• algebraic techniques
• functions and graphs
• an informal discussion of limits
• techniques of differentiation and integration
• Maclaurin and Taylor expansions
• geometrical applications

Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.

The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.

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9781848008434

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Reviews

From the reviews: <p> The book is aimed at beginning university students as a introductory calculus textbook a ] . Undoubtedly it is a clearly written exposition of the most typical topics of calculus ... full of good examples, with plenty of exercises and answers to them. ... Summing up, the reviewed book is a decent item, which might be recommended not as a main textbook for an introductory calculus course, but as a additional source mainly for practising typical procedures of differentiation and integration. (Piotr Zarzycki, The Mathematical Gazette, Vol. 92 (525), 2008)

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