Introduction to Analysis, An

by William R. Wade

User-friendly -- yet rigorous -- in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes many complicated proofs with a "Strategy" which motivates the proof, shows why it was chosen, and why it should work. Examples follow many theorems, showing why each hypothesis is needed, allowing readers to remember the hypotheses by recalling the examples. Proofs are presented in complete detail, with each step carefully documented, and proofs are linked together in a way that teaches readers to think ahead. Physical interpretations are used to examine some concepts from a second or third point of view. Includes over 200 worked examples and over 600 exercises. Provides extensive coverage of multidimensional analysis.

Genres: Mathematics, Textbooks, Science, Nonfiction

520 pages, Hardcover

First published August 1, 1994

Reviews

[Felix303 · Rating 4 out of 5]

I covered a bulk of the book in my analysis course, as well as more in free time. The book provides a solid introduction to analysis. Compared to, say, Abbott's understanding analysis, its less of a hand-held experience, and the author expects the reader to take greater responsibility of their own learning.
However, I personally liked the rigorous and concise writing style. It provides a nice middle ground between Abbott's book, and Baby Rudin, being approachable by beginners, while accommodating the developing skills of the reader.

All in all, I would recommend this book to the dedicated beginner looking for a solid introduction to analysis.

[Fatima · Rating 3 out of 5]

wasn't a huge fan and ended up relying the lecture notes by my professor.

[Patrick Hettinger · Rating 3 out of 5]

This one isn't quite a page-turner. But if you want to be able to prove why calculus works, this is a place to start!