Elementary Analysis (eBook)

The Theory of Calculus

Kenneth A. Ross (Autor)

eBook Download: PDF

2013 | 2nd ed. 2013
XII, 412 Seiten
Springer New York (Verlag)
978-1-4614-6271-2 (ISBN)

Infos

For three decades, this classic has been a must-have textbook for transitional courses from calculus to analysis, celebrated for its clear style and simple proofs. This edition adds material on the irrationality of pi, the Baire category theorem and more.

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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs.  Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus.  Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs.  New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions. Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and. has succeeded admirably."—MATHEMATICAL REVIEWS

Autor

Kenneth A. Ross is currently an emeritus professor of mathematics at the University of Oregon.Jorge M. López is currently professor of mathematics at the University of Puerto Rico.

Inhalt

Preface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.

Produkt-Details

• Reihe/Serie: Undergraduate Texts in Mathematics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Bolzano-Weierstrass theorem • Continuous functions • Differentiation • elementary analysis • fundamental theorem of calculus • Integration • L'Hospital's rule • limits of sequences • mean • mean value theorem • monotone subsequences • nowhere-differentiable functions • power series • rational zeros theorem • Riemann integral • Riemann-Stieltjes integral • Taylor's theorem
• ISBN-10: 1-4614-6271-1 / 1461462711
• ISBN-13: 978-1-4614-6271-2 / 9781461462712