This user-friendly introduction to the methods of differential and integral calculus of one real variable, eases the transition from high school to university math. It presents new ideas in the context of existing mathematical experience, building on students' A-level knowledge and extending it to the level encountered in first year degree courses in mathematics and the physical sciences.

The emphasis is on helping readers to understand the critical ideas and developing their manipulative skills, so topics are explained using worked examples and exercises.

An informal and gentle introduction that helps readers to understand the critical ideas as well as develop their manipulative skills Adopts a user-friendly approach, with an emphasis on worked examples and exercises, rather than abstract theory The use of Maple can be integrated into the text to provide an additional aid to teaching and learning Supported by additional exercises, exam questions, and more detailed solutions available via the web Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Autorentext

Keith Hirst is an experienced author and lecturer, with many years' experience teaching undergraduate courses. His research interests include Mathematics Education and Teaching Methods in Higher Education, with particular emphasis on the school / university interface. Keith also researched the area of learning problems in calculus as part of an investigation into undergraduates' conceptions of mathematical ideas. In 2000, he was awarded one of the first prestigious National Teaching Fellowships by the Institute of Learning and Teaching, to develop a database of undergraduate teaching resources.

Klappentext
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.

Inhalt
Functions and Graphs.- Limits of Functions.- Differentiation.- Techniques of Differentiation.- Applications of Differentiation.- Maclaurin and Taylor Expansions.- Integration.- Integration by Parts.- Integration by Substitution.- Integration of Rational Functions.- Geometrical Applications of Integration.