What Is Calculus?: From Simple Algebra To Deep Analysis
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A01=R Michael Range
Analysis
Author_R Michael Range
Calculus
Category=PBK
Completeness
Continuity
Definite Integrals
Differentiability
Double Points
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exponential Functions
Fundamental Theorem of Calculus
Taylor Series
Product details
- ISBN 9789814644471
- Publication Date: 06 Oct 2015
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
