What Is Calculus?: From Simple Algebra to Deep Analysis

ISBN-13: 9789814644471 / Angielski / Twarda / 2016 / 372 str.

R. Michael Range

Opis

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.