Description
Book SynopsisTrade ReviewFoundations of Analysis is an excellent new text for undergraduate students in real analysis. More than other texts in the subject, it is clear, concise and to the point, without extra bells and whistles. It also has many good exercises that help illustrate the material. My students were very satisfied with it." - Nat Smale, University of Utah
"I have taught our Foundations of Analysis course (based on Joe Taylor's book) several times recently, and have enjoyed doing so. The book is well-written, clear, and concise, and supplies the students with very good introductory discussions of the various topics, correct and well-thought-out proofs, and appropriate, helpful examples. The end-of-chapter problems supplement the body of the text very well (and range nicely from simple exercises to really challenging problems)." - Robert Brooks, University of Utah
"An excellent text for students whose future will include contact with mathematical analysis, whatever their discipline might be. It is content-comprehensive and pedagogically sound. There are exercises adequate to guarantee thorough grounding in the basic facts, and problems to initiate thought and gain experience in proofs and counterexamples. Moreover, the text takes the reader near enough to the frontier of analysis at the calculus level that the teacher can challenge the students with questions that are at the ragged edge of research for undergraduate students. I like it a lot." - Don Tucker, University of Utah
"My students appreciate the concise style of the book and the many helpful examples." - W.M. McGovern, University of Washington
Table of Contents
- Preface
- The real numbers
- Sequences
- Continuous functions
- The derivative
- The integral
- Infinite series
- Convergence in Euclidean space
- Functions on Euclidean space
- Differentiation in several variables
- Integration in several variables
- Vector calculus
- Degrees of infinity
- Bibliography
- Index
