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

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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.

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

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.

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