|
This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors. |
|
View the Preface, Table of Contents, Introduction, and Index. |
|
This book comes from a live human being, not a publisher's marketing group... Estep has a very radical philosophy of teaching. For each topic, he frankly tells the reader why we want to do this, why we need to do it this way, and then he actually does it! Completely, correctly, and readably! ... All the details are there, the proofs are complete. Even more impressive, their motivation is there first. The student will go through the details, because he has seen why it makes sense to do that... For the reader that wants to teach himself analysis, I can think of no better book for self-study. Most books leave a lot of the heuristics and motivation to be supplied in the classroom. And most books leave out many proofs that a beginner might have trouble finding on his own. This book, having the heuristics, the motivation, and the details of the proofs, could be read independently and understood all the way through. SIAM REVIEW (Click here for full review) |
|
Estep combines the basic ideas of real analysis and numerical analysis in an applied framework ...beautifully presented in the context of a fundamental approach to applied mathematical problem solving, which is to approximate the solution of a physical model. The book is written in an engaging manner... Background and review material and numerous examples, including visualizations and alternate explanations of some key ideas, are provided in a very appealing manner. Abstract concepts are carefully explained and supported with a wealth of examples and illustrations and a wonderful collection of problems, a few elementary enough for any beginner. Summing Up: Highly recommended. CHOICE Review (Click here for full review) |
| ... The book contains most of the classical topics in real analysis,
but they are presented in the context of approximating solutions of
physical models, a fundamental problem in applied mathematics... I confess
that when I first started reading this book I was intrigued by the new
approach of real analysis but did not quite see what it might be good
for. In the end, however, I was convinced that it could be a very good
text book, especially in courses taken mostly by engineering majors:
I am sure these students would find the approach of the book attractive
and motivating.
MAA Online Book Review (Click here for full review) |
| This book is intended either for an honors calculus sequence or for the first real analysis course for mathematics majors who have completed the calculus sequence... There is an abundance of exercises ranging from simple computations to estimates to computational projects. There is emphasis on providing explanation in solutions, and some exercises call for proofs of theorems. It should be an interesting book for either of the intended uses.
AMS Mathematical Reviews (Click here for full review) |
The book's inviting style, attention to pedagogy, frequent historical and "cultural" asides, and other unusual features all add to its value, and argue for its presence in every library where undergraduates and their teachers browse. Review in the American Mathematical Monthly (Click here for full review) |