TY  - GEN
AU  - Keisler,H.Jerome
TI  - Elementary calculus: An infinitesimal approach
SN  - 9780486484525
U1  - 515 22
PY  - 2012///
CY  - New York
PB  - Dover Publications
KW  - Cálculo
N1  - Include appendix and index. - - Appendix tables; Real and hyperreal numbers. - - Continuous funtions. - - Applications of the integral. - - Trigonometric funtions. - - Vectors. - - Partial differentation. - - Multiple integrals. - - Vector calculus. - - Differantial equations
N2  - This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods. Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences
ER  -