This book takes a rigorous approach to, and therefore creates a deeper understanding of, the usual topics handled in one-dimensional calculus--limits, continuity, differentiation, integration, and infinite series. The text was designed to bridge the gap between intuitive calculus courses normally offered at the undergraduate level and the sophisticated analysis courses offered at the senior or graduate level. The author wrote the book with two goals in mind: the development of a rigorous foundation for the basic topics of analysis, and the less tangible acquisition of an accurate intuitive feeling for analysis.
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Book Description
Editorial Reviews
About the Author
Ph.D., University of Kansas
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Most Helpful Customer Reviews
8 of 8 people found the following review helpful:
5.0 out of 5 stars
Excellent,
This review is from: Introduction to Analysis (Contemporary undergraduate mathematics series) (Hardcover)
At first glance, the book appears too thin. But once you've delved a few pages into it, you immediately recognize that the author has simply mastered the art of brevity - while remainining eminently readable. The book covers all the material needed for an undergraduate analysis course - and covers it extremely well. The proofs are easy to follow and extremely instructive, so that the book can also be used in a "Bridge to Advanced Mathematics" or "How to do Proofs" that some schools offer to their math majors to ease the transition from problem-based lower-division courses to proof-based upper-division courses.
5 of 5 people found the following review helpful:
4.0 out of 5 stars
A compact and well written book.,
By Abdul.Aziz.Ali@statistics.gu.se (Gothenburg, Sweden) - See all my reviews
This review is from: Introduction to Analysis (Hardcover)
The proofs are well structured and easy to follow. The techniques used in the proofs lend themselves for use in other situations. A lot of information is embeded in the exercises which keep the students alert and focused and at the same time saves time and space. A good book for undergraduates in mathematical analysis.
7 of 8 people found the following review helpful:
3.0 out of 5 stars
Introduction to Analysis,
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This review is from: Introduction to Analysis (Hardcover)
Although this text has quite a few good projects and problems, it is a bit too concise particularly for the student who is new to anaylsis. While all the major theorems are presented with proofs, some of the proofs are quite difficult to follow and many involve "hand-waving" in the proof. For the new student, this may cause a bit of confusion. Also, when a student goes to complete the homework, they may not be as clear and rigorous as necessary. It could also do a bit more in ways of visual arguments to help clarify the concepts being proved. The projects are probably the best part of the text because they have some of the classic calculus concepts built up by the student. I would have also appreciated a selected solutions or more helpful hints on some of the more difficult homework problems.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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conditional convergence, uniform continuity, converges iff, accumulation point, convergent infinite series, prove that the sequence, nth partial sum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Suppose, Proof Let, Proof Choose, Proof Assume, Taylor's Theorem, Proof Define, The Riemann Integral, Mean-Value Theorem, Limits of Functions, Chain Rule, Fundamental Theorem of Integral Calculus, Prove Theorem, Abel's Theorem, Rolle's Theorem, Bolzano-Weierstrass Theorem, L'Hospital's Rule, Arithmetic Operations, Proof First, Bolzano's Theorem, Riemann Sums, Use Exercise, Algebra of Integrable Functions, Properties of Continuous Functions, Intermediate-Value Theorem, Proof By Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
conditional convergence, uniform continuity, converges iff, accumulation point, convergent infinite series, prove that the sequence, nth partial sum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Suppose, Proof Let, Proof Choose, Proof Assume, Taylor's Theorem, Proof Define, The Riemann Integral, Mean-Value Theorem, Limits of Functions, Chain Rule, Fundamental Theorem of Integral Calculus, Prove Theorem, Abel's Theorem, Rolle's Theorem, Bolzano-Weierstrass Theorem, L'Hospital's Rule, Arithmetic Operations, Proof First, Bolzano's Theorem, Riemann Sums, Use Exercise, Algebra of Integrable Functions, Properties of Continuous Functions, Intermediate-Value Theorem, Proof By Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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