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  1. Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
    Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
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  • Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)

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Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)

by Omar Hijab (Author) Format: Hardcover
5.0 out of 5 stars (3)
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Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.
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  1. ISBN-10
    0387693157
  2. ISBN-13
    978-0387693156
  3. Edition
    2nd ed.
  4. Publisher
    Springer
  5. Publication date
    May 15, 2007
  6. Part of series
    Undergraduate Texts in Mathematics
  7. Language
    English
  8. Dimensions
    6 x 0.75 x 9.25 inches
  9. Print length
    352 pages
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Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
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Editorial Reviews

From the Back Cover

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This second edition includes corrections as well as some additional material.

Some features of the text:

* The text is completely self-contained and starts with the real number axioms;

* the integral is defined as the area under the graph, while the area is defined for every subset of the plane;

* there is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero;

* there are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more;

* traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals;

* there are 366 problems.

About the first edition:

This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, "Why is it never done like this?"

John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper

Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ May 15, 2007
  • Edition ‏ : ‎ 2nd ed.
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 352 pages
  • ISBN-10 ‏ : ‎ 0387693157
  • ISBN-13 ‏ : ‎ 978-0387693156
  • Item Weight ‏ : ‎ 7.6 ounces
  • Dimensions ‏ : ‎ 6 x 0.75 x 9.25 inches
  • Part of series ‏ : ‎ Undergraduate Texts in Mathematics
  • Best Sellers Rank: #4,699,250 in Books (See Top 100 in Books)
  • Customer Reviews:
    5.0 out of 5 stars (3)

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  1. O. Hijab

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Customer reviews

5 out of 5 stars
3 global ratings

Top reviews from the United States

  • Gary
    5 out of 5 stars
    refreshing, albeit terse, exposition
    Reviewed in the United States on January 1, 2014
    Format: Hardcover
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    A stimulating and thought provoking textbook. I greatly enjoyed study of this book (that is, irrespective of an assigned course). The topics presented are a bit off of the beaten path for an elementary analysis text. The initial chapter will be the hardest. I say this: if you can assimilate the initial thirty-pages (chapter one) and complete those exercises, then all else will flow with relative ease (but, not necessarily easy !). Limits, Sequences and Series are presented in quick succession, proffered ever so clearly. A chapter on continuity follows, then differentiation. Trigonometric functions are given a nice treatment. Chapter four: Integration begins with area and concludes with so-called "method of exhaustion." Fifth (and final) chapter is the best of the book, applying all of the previous material to topics of classical analysis: Gamma, Pi, Gauss AGM, Infinite products, Zeta Functions, to name a few of those topics.

    Solutions to the problems are included (an incentive for self-study).

    Aside: My interest was piqued by a book review in the American Mathematical Monthly (Volume 105, Number 7),

    it doesn't hurt to see another viewpoint of the book. I quote from that review: "I believe that Hijab's book was written

    less as a textbook and more as a way of making love to his subject." (Steven G. Krantz, page 678).

    After studying the text, you, too, will decide if it is of your ilk.

    Needless to say, at least this is an alternative for an adventurous undertaking.

    The effort is to be applauded.

    7 people found this helpful
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  • Kersi Von Zerububbel
    5 out of 5 stars
    Superb for self-study. Clearly written with worked examples.
    Reviewed in the United States on May 17, 2011
    Format: Paperback
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    I have been using this text for the last 9 months as a self-study exercise in Analysis. I had never heard of the author nor this title but came across it by accident at a book store here in San Diego, CA.

    This is an excellent text for someone interested in Analysis and the theory behind the same. Especially if you want to prepare yourself for college courses in the fall this text will be great to go through all summer. Be aware that this is not just an introductory Calculus text, of which there are many, rather this is a Calculus text with emphasis on Analysis. I found this book far more manageable than say Courant's "Differential and Integral Calculus" which is a classic Analysis text but is meant mainly for courses in pure mathematics and thus above my capabilities in many chapters.

    The writing is EXCELLENT and very amenable for the self-learner. If you are willing to put in the effort this book is great.

    14 people found this helpful
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