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Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)

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en Limba Engleză Hardback – 17 Apr 2013
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
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Specificații

ISBN-13: 9781461462705
ISBN-10: 1461462703
Pagini: 424
Ilustrații: XII, 412 p.
Dimensiuni: 155 x 235 x 32 mm
Greutate: 0.75 kg
Ediția: 2nd ed. 2013
Editura: Springer
Colecția Springer
Seria Undergraduate Texts in Mathematics

Locul publicării: New York, NY, United States

Public țintă

Lower undergraduate

Cuprins

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.

Recenzii

From the reviews of 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, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."
—MATHEMATICAL REVIEWS
"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails."
—Allen Stenger (The Mathematical Association of America, June, 2008)

Notă biografică

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.

Textul de pe ultima copertă

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


Caracteristici

Revised and updated second edition with new material
Text for a transition course between calculus and more advanced analysis courses
Contains new material on topics such as irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions
Includes new examples and improved proofs
Includes supplementary material: sn.pub/extras