Calculus of One Variable

Keith E. Hirst - Collection Springer Undergraduate Mathematics Series (SUMS)

270 pages, parution le 04/11/2005

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Résumé

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.

Written for: 1st year undergraduate students in mathematics, engineering and science

Sommaire

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
Answers to Selected Exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Keith E. Hirst
Collection	Springer Undergraduate Mathematics Series (SUMS)
Parution	04/11/2005
Nb. de pages	270
Format	18 x 23,5
Couverture	Broché
Poids	455g
Intérieur	Noir et Blanc
EAN13	9781852339401
ISBN13	978-1-85233-940-1