Elementary Calculus (eBook)

H. Jerome Keisler (Autor)

eBook Download: EPUB

2013 | 3rd Edition
1008 Seiten
Dover Publications (Verlag)
978-0-486-31046-6 (ISBN)

Infos

This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including approximation problems, vectors, partial derivatives, and multiple integrals. 2007 edition.

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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.

Autor

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.

Inhalt

Introduction1. Real and Hyperreal Numbers2. Differentiation3. Continous Functions4. Integration5. Limits, Analytic Geometry, and Approximations6. Applications of the Integral7. Trigonometric Functions8. Exponential and Logarithmic Functions9. Infinite Series10. Vectors11. Partial Differentiation12. Multiple Integrals13. Vector Calculus14. Differential EquationsEpilogueAppendix: TablesAnswers to Selected ProblemsIndex

Produkt-Details

• Erscheint lt. Verlag: 22.4.2013
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 170 x 170 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: applications of calculus • approximation problems • Basic Concepts • Calculus • central concepts • Continuity • Derivatives • elementary calculus • infinitesimals • integrals • Math • Mathematics • Methods • Motivation • Multiple integrals • ordinary calculus • partial derivatives • series • students and teachers • Textbook • traditional approach • traditional limit concept • transcendental functions • Vectors
• ISBN-10: 0-486-31046-9 / 0486310469
• ISBN-13: 978-0-486-31046-6 / 9780486310466