K. E. Hirst

Calculus of One Variable (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 268
• Erscheinungstermin: 17. Dezember 2005
• Englisch
• ISBN-13: 9781846282225
• Artikelnr.: 44134305

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

From the reviews:

"The book is aimed at beginning university students as a introductory calculus textbook ... . 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)