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What Is Calculus?: From Simple Algebra To Deep Analysis

SPAR
kr 146

What Is Calculus?: From Simple Algebra To Deep Analysis

 

This unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are 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 using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions.

The author carefully develops the necessary foundations while minimizing the use of technical language. He 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 a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.

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This unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are 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 using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions.

The author carefully develops the necessary foundations while minimizing the use of technical language. He 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 a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.

Produktdetaljer
Sprog: Engelsk
Sider: 372
ISBN-13: 9789814644471
Indbinding: Hardback
Udgave:
ISBN-10: 9814644471
Udg. Dato: 6 okt 2015
Længde: 25mm
Bredde: 237mm
Højde: 161mm
Forlag: World Scientific Publishing Co Pte Ltd
Oplagsdato: 6 okt 2015
Forfatter(e) R Michael (State Univ Of New York At Albany Range, R Michael Range


Kategori Regning og matematisk analyse


Sprog Engelsk


Indbinding Hardback


Sider 372


Udgave


Længde 25mm


Bredde 237mm


Højde 161mm


Udg. Dato 6 okt 2015


Oplagsdato 6 okt 2015

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