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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. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book.
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.