PDF Ebook Advanced Calculus: An Introduction to Analysis, by Watson Fulks
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Advanced Calculus: An Introduction to Analysis, by Watson Fulks
PDF Ebook Advanced Calculus: An Introduction to Analysis, by Watson Fulks
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Introduces analysis, presenting analytical proofs backed by geometric intuition and placing minimum reliance on geometric argument. This edition separates continuity and differentiation and expands coverage of integration to include discontinuous functions. The discussion of differentiation of a vector function of a vector variable has been modernized by defining the derivative to be the Jacobian matrix; and, the general form of the chain rule is given, as is the general form of the implicit transformation theorem.
- Sales Rank: #1430667 in Books
- Published on: 2016-01-05
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 9.23" h x 1.73" w x 6.75" l, 2.64 pounds
- Binding: Hardcover
- 752 pages
From the Publisher
Introduces analysis, presenting analytical proofs backed by geometric intuition and placing minimum reliance on geometric argument. This edition separates continuity and differentiation and expands coverage of integration to include discontinuous functions. The discussion of differentiation of a vector function of a vector variable has been modernized by defining the derivative to be the Jacobian matrix; and, the general form of the chain rule is given, as is the general form of the implicit transformation theorem.
Most helpful customer reviews
1 of 1 people found the following review helpful.
A useful introduction to real analysis
By physics student
I used the first edition of this book way back in 1963. It was good for an introduction to real analysis and advanced calculus - not stellar, but I still consult it from time to time. It gives a good account of the Riemann integral, and of Fourier series.
The fact that it is still in print, in the 3rd edition, says much for it.
1 of 2 people found the following review helpful.
Good book for physics majors
By Mark A. Kirkland
This is a very good book for physics majors. It covers all the topics in freshman calculus at an advanced level including vector calculus, Fourier series, integral representation of functions and some special functions. Working through this text along with a book on complex variables will prepare you for a course in Arfken.
0 of 1 people found the following review helpful.
I learned a ton
By bearieq
First the bad points, then the good.
Worst point: This text (I read the third edition) is riddled with typos. The worst typo of all occurs in the implicit function theorem, in which both the statement of the theorem and the proof are incorrect. The error that Fulks makes in this theorem arises directly from his poor statement of the inversion theorem. Those are the worst two offenders; there are many others.
It is interesting to note that the error in Fulks's statement of the implicit function theorem is obvious if one has a good geometric intuition of that theorem. Indeed, in many cases where good geometric intuition would greatly help the reader to understand what is going on, Fulks fails to present that intuition. I understand and agree with his goal of presenting arithmetical rather than geometrical proofs. But the use of arithmetical proofs makes it *more*, not *less* important that the motivating discussions present the best possible geometrical intuition underlying the proofs. As I read Fulks (particularly the section on vector calculus), I found myself frequently consulting my Stewart "Calculus" textbook to refresh my memory of the geometrical intuition of the topic.
Paradoxically, these major flaws actually caused me to learn the material *better* than if the book had not had those flaws. Every time I hit a typo, I had to stop and figure out the correction; every time a discussion or proof was not geometrically obvious to me, I had to stop and find a geometric intuition (sometimes by consulting Stewart, but often just by thinking). All this work made me understand the material much better than I ever have.
Talking about work, one of the things I like a lot about the book is that it expects the reader to love math and to be willing to work at learning it. It does not spoonfeed the reader. It is a math book written for people who like and are good at math, which is a wonderful thing to read.
There are many other things that I like about the book. I like Fulk's writing style; it's as if he is standing in front of the blackboard and talking to me. I like how he consistently uses the Jacobian in all of the vector calculus instead of presenting a bunch of results that are expressed in terms of cross products and thus apply only to E3. And most of all I love his overall organization, which very, very clearly shows how each new topic and result depends on previous topics and results. It is quite a beautiful thing to watch him build the ever-upward-spiraling tower of mathematics.
Incidentally, until I read this book I never realized just how many proof are omitted in basic calculus textbooks. And not just the proofs themselves, but also the significant amount of underlying mathematical machinery (e.g., cluster points, limit supremum, Heine-Borel, ...) that those proofs require. Reading the proofs and learning the underlying machinery has greatly improved my understanding of calculus, and has opened my eyes to what awaits me in higher analysis.
PS. I would have really, really have liked a solution manual, both to check my solutions and to read the solutions to those problems that I was simply unable to solve or find via google.
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