What Is Calculus?: From Simple Algebra to Deep Analysis

Range, R. Michael

ISBN 10: 981464448X / ISBN 13: 9789814644488

Editore: World Scientific Pub Co Inc, 2016

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280 pages. 10.50x7.50x1.00 inches. In Stock.

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Dati bibliografici

• Titolo: What Is Calculus?: From Simple Algebra to Deep Analysis
• Editore: World Scientific Pub Co Inc
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 981464448X
• ISBN 13: 9789814644488
• Rilegatura: Paperback
• Condizione: Brand New

Descrizione articolo

Riassunto

This unique book provides a new and well-motivated introduction to calculus and analysis that are historically significant fundamental areas of mathematics and widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without ever using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject.The author carefully develops the necessary foundations while minimizing the use of technical language, and expertly guides the reader to deep fundamental analysis results, including completeness, key differential equations, definite integrals, Taylor series for standard functions, and the Euler identity. This pioneering book takes the sophisticated reader from simple familiar algebra to the heart of analysis. Furthermore, it should be of interest as supplementary reading and source of new ideas for high school teachers, and for students and instructors of calculus and analysis.

Recensione

It is a well-written and worthwhile addition to the long list of books on calculus. The treatment of derivatives and the basics of real analysis are excellent. --Professor John P D'Angelo, University of Illinois at Urbana Champaign, USA

The book can be recommended for interested students as well as for teachers in mathematical analysis. --Zentralblatt MATH

It certainly would provide excellent corrective revision of calculus for those who have been taught it simplistically. Another attractive feature of the book is its historical element, which includes reference to the algebraic/geometric method of Apollonius for finding tangents etc. This, together with the above-mentioned features, make this book a uniquely imaginative introduction to real analysis alongside a cogent account of the principles, and applications, of differentiation and the Riemann integral. --Mathematical Association of America