Elementary Analysis
The Theory of Calculus
Seiten
2013
|
2nd ed. 2013
Springer-Verlag New York Inc.
978-1-4614-6270-5 (ISBN)
Springer-Verlag New York Inc.
978-1-4614-6270-5 (ISBN)
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.
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.
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.
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.
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.
| Reihe/Serie | Undergraduate Texts in Mathematics | Undergraduate Texts in Mathematics |
|---|---|
| Zusatzinfo | XII, 412 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Analysis; Handbuch/Lehrbuch • Bolzano-Weierstrass theorem • Continuous functions • Differentiation • elementary analysis • fundamental theorem of calculus • Integration • L'Hospital's rule • limits of sequences • mean value theorem • monotone subsequences • nowhere-differentiable functions • power series • rational zeros theorem • Riemann integral • Riemann-Stieltjes integral • Taylor's theorem |
| ISBN-10 | 1-4614-6270-3 / 1461462703 |
| ISBN-13 | 978-1-4614-6270-5 / 9781461462705 |
| Zustand | Neuware |
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