Inside Calculus (Undergraduate Texts in Mathematics)

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Product Description

The approach here relies on two beliefs. The first is that almost nobody fully understands calculus the first time around. The second is that graphing calculators can be used to simplify the theory of limits for students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build an understanding of the notion of limit and other theoretical concepts. Aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient, the text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course. Suitable as the "content" text for a transition to upper level mathematics course.

Inside Calculus (Undergraduate Texts in Mathematics) Review

Ok so the previous reviewer is quite obviously not a mathematician and doesn't seem to understand that mathematics (pure math anyway) IS about theory and proofs. This book is probably the best introduction to real analysis that I have ever seen, I would give anything to go back in time and have my professors use this book as a supplement in my calculus classes. As it is, I tutor a few dozen real analysis students every semester and that task has become profoundly easier after discovering this book, I simply tell them to follow in this book the material they cover in class. By seeing a handful of computational examples before delving into the theoretical homework problems, they gain a great deal of intuition about how to write their proofs and apply their knowledge. I think Dr. Exner has done the world of math a great service and I HIGHLY recommend this book for a) serious math students to follow along with during their calculus classes, b) students of real analysis who are having a difficult time getting an intuitive grasp of the concepts covered in their classes, and c) as an analysis supplement for those who are interested in self-study.

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