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Elementary Calculus: An Infinitesimal Approach: Dover Books on Mathematics

Autor H. Jerome Keisler
en Limba Engleză Paperback – feb 2012
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.
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Specificații

ISBN-13: 9780486484525
ISBN-10: 0486484521
Pagini: 913
Dimensiuni: 173 x 251 x 51 mm
Greutate: 1.57 kg
Ediția:3rd ed.
Editura: Dover Publications
Seria Dover Books on Mathematics

Locul publicării:Mineola, NY, United States

Descriere

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.

Cuprins

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