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.
By:
H. Jerome Keisler,
Mathematics
Imprint: Dover Publications Inc.
Country of Publication: United States
Edition: 3rd ed.
Dimensions:
Height: 230mm,
Width: 160mm,
Spine: 50mm
Weight: 1.420kg
ISBN: 9780486484525
ISBN 10: 0486484521
Series: Dover Books on Mathema 1.4tics
Pages: 1008
Publication Date: 15 February 2012
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Paperback
Publisher's Status: Unspecified
Introduction 1. Real and Hyperreal Numbers 2. Differentiation 3. Continous Functions 4. Integration 5. Limits, Analytic Geometry, and Approximations 6. Applications of the Integral 7. Trigonometric Functions 8. Exponential and Logarithmic Functions 9. Infinite Series 10. Vectors 11. Partial Differentiation 12. Multiple Integrals 13. Vector Calculus 14. Differential Equations Epilogue Appendix: Tables Answers to Selected Problems Index
H. Jerome Keisler was a longtime professor at the University of Wisconsin, Madison. He pursued his Ph.D. under the direction of Alfred Tarski at the University of California, Berkeley, and his research included model theory and nonstandard analysis.
