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eBook The Way of Analysis ePub

eBook The Way of Analysis ePub

by Robert S. Strichartz

  • ISBN: 0867204710
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Robert S. Strichartz
  • Language: English
  • Publisher: Jones & Bartlett Pub; First Edition edition (April 1, 1995)
  • Pages: 739
  • ePub book: 1956 kb
  • Fb2 book: 1370 kb
  • Other: lrf txt lrf rtf
  • Rating: 4.5
  • Votes: 847

Description

Download books for free. This introduction to real analysis contains thorough and complete proofs with lively and generous explanation to guide the reader through the foundations and the way of analysis.

Download books for free. Real analysis, in one and several variables, is developed from the construction of the real number system to an introduction to the Lebesgue integral. Additionally, there are three chapters on applications of analysis, ordinary differential equations, Fourier series, and curves and surfaces, to show how the techniques of analysis are used in concrete settings.

Analysis was developed over centuries and without sufficient motivation and examples it is just impossible to come to grips with the subject.

Find all the books, read about the author, and more. Are you an author? Learn about Author Central. Robert S. Strichartz (Author). Analysis was developed over centuries and without sufficient motivation and examples it is just impossible to come to grips with the subject. A bit more explanation never hurt anyone and this book has a lot of detail and points out subtleties that are easily missed if you read some of the other books on analysis. One example is the difference between a limit point and the limit of a sequence. I did not know the difference till I read this book.

by. Strichartz, Robert S. Publication date. Mathematical analysis. Boston : Jones and Bartlett Publishers. inlibrary; printdisabled; trent university;. Kahle/Austin Foundation.

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Robert S. Strichartz. The Text Provides Proofs Of All Main Results, As Well As Motivations, Examples, Applications, Exercises, And Formal Chapter Summaries. Additionally, There Are Three Chapters On Application Of Analysis, Ordinary Differential Equations, Fourier Series, And Curves And Surfaces To Show How The Techniques Of Analysis Are Used In Concrete Settings.

The Way of Analysis : Principles of Math Analysis. by Robert S.

Robert Stephen Strichartz (born October 14, 1943, in New York City) is an American mathematician, specializing in mathematical analysis. In 1966 Strichartz received his PhD from Princeton University under Elias Stein with thesis Multipliers on generalized Sobolev spaces. Moore Instructor at Massachusetts Institute of Technology. He is a professor at Cornell University.

8. The Way of Analysis (Paperback).

The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. 8. Published by Jones and Bartlett Publishers, Inc, United States (2000). ISBN 10: 0763714976 ISBN 13: 9780763714970.

Finding books BookSee BookSee - Download books for free. 1. 2 Mb. The way of analysis. 3 Mb. A Guide to Distribution Theory and Fourier Transforms (Studies in Advanced Mathematics). 1 Mb. A guide to distribution theory and Fourier transforms. Category: M Mathematics, MC Calculus, MCf Functional analysis. 6 Mb.

Mathematics is a way of thought. Attaining a deep understanding of mathematics is more than mastering a collection of theorems, definitions, problems, and techniques; it is understanding how theorems and definitions fit together with the overall strategy of arguments presented. This introduction to real analysis contains thorough and complete proofs with lively and generous explanation to guide the reader through the foundations and the way of analysis. Real analysis, in one and several variables, is developed from the construction of the real number system to an introduction to the Lebesgue integral. Additionally, there are three chapters on applications of analysis, ordinary differential equations, Fourier series, and curves and surfaces, to show how the techniques of analysis are used in concrete settings.

Comments

Quinthy Quinthy
OK, so what does that title mean? I was a graduate student in math at Cornell in the early 1980's and a TA for Bob Strichartz when he used a set of original lecture notes--which eventually developed as "The Way of Analysis"--for an undergraduate analysis course there. The "standard" book for that course at the time was Rudin's "Principles of Mathematical Analysis" a.k.a. "Baby Rudin".

Looking through my copy of the 1995 edition of the finished book, I recognize Strichartz's method of showing students "the way" to think about--and eventually try to discover for themselves--what theorems might be true, what definitions might be useful, what arguments might be fruitful, etc. As the grader for the course, I had an opportunity to see how many students (not all of whom were math majors) were able to benefit from the motivation provided in the notes to get a real feel for the subject. Moreover, even as (at that time) a third-year graduate student specializing in analysis myself, I found that the notes provided a context that I had not seen before in other analysis books.

One criticism appearing in some of the other reviews is that the exposition in the book is often verbose--thus not providing a useful reference book. I do agree with this to some extent--a few definitions are not clearly marked as such in boldface type when the reader first encounters them. Nonetheless, the chapter summaries do provide lists of definitions and theorems presented in each chapter. And for those interested mainly in a reference text for undergraduate analysis, choices such as Baby Rudin and Apostol's "Mathematical Analysis" are readily available.

However, for an advanced undergraduate level analysis course--particularly for students who have not already had an introduction to reading and writing proofs--this book is to be highly recommended.
Nagor Nagor
This book has step-by-step proofs that are easy to follow. I really love this book. It is probably one of the best math textbook I have read so far in my undergrad math major.
Fegelv Fegelv
on time and as described
Gunos Gunos
There are many fine books on analysis out there. If you're just looking for something for reference, those by Rudin, or Kolmogorov, or others would work just fine. But if you want to LEARN analysis, if you want to actually understand the motivation behind it, then this is, simply put, the best book out there.
I've used this book along with Kolmogorov's for about a term and a half now in my classical analysis class. As an example of the difference between them, consider their coverage of the implicit function theorem, one of the most fundamental theorems of behind the study of surfaces. Strichartz devoted two sections to this theorem, explaining what it was, what it's motivation was, and even how the proof related to the Newton's Method of First-Year Calculus. I came away from the text feeling I actually understood what the theorem meant and how it fit into the rest of Analysis.
Kolmogorov left it as an exercise to the reader.
This is the kind of textbook you can bring with you on a car trip and easily study along the way. It takes an informal writing style and from the beginning is focused on making sure you, as the reader, understand not just the theorems and proofs, but the concepts of real analysis as well. Every new idea is given not only with a What or a How, but with a Why as well, preparing the reader to ask themselves the same questions as they progress further.
This is not to say the book is without rigor though. The theorems and the proofs are still there, just enriched by the other material contained within the book, and anyone mastering this book will be well prepared for future analysis courses, both mathematically and in their way of thinking about the subject.
Hinewen Hinewen
Strichartz's book contains many clear explanations, and most importantly, contains informal discussions which reveal the motivations for the definitions and proofs. I believe the "informalness" of the book with the insights make this book a very appropriate text for those taking their first rigorous mathematics class. And this text is definitely much better than many of the texts that target that audience.
The format of the book is more disorganized than the standard texts like Rudin, but makes it more likely that it will be read and thoroughly digested, instead of sitting on the shelf. That said, one will probably never want to look at the book again after one has learned the material. If one does so, like I did, one will gasp in horror at the lack of conciseness, brevity, etc., and then rewrite one's Amazon review, like I am.
While trying to do the homeworks, I noticed that because not every result was made into a lemma or theorem, this made it somewhat difficult in finding the necessary info; however, the bulk of the definitions and theorems are listed in the chapter summaries.
The proofs in the book are fairly standard and repetitive. If you want to see cleverness that makes one gasp, see Rudin.