There are many excellent texts. I've used Edwards as a primary text for an advanced calculus course and I will agree it is a bit short on problems. You might like Kaplan's text, it's more on the math for scientist and engineers side of the advanced calculus spectrum. On the other hand, the text by Hans Sagan is really something, very complete lots of details.

- Advanced Calculus of Several Variables!
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I recently got Cartan's advanced calculus text which is available as a Dover. That text is very centered around the concept of differential forms, worth a look. It has a few hundred more problems for you to chew on. The text by Flanders on differential forms is a bit terse, but once you understand the calculations it's quite deep. I suppose the question is what are you after? Basics of Differential Forms?

## Advanced calculus of several variables - CERN Document Server

If I have any trouble with Edwards, it is that the analysis is a bit scattered in that text. As an example, the proof of the implicit or inverse mapping theorems ultimately rests on an iterative sequence converging to the desired map. However, ideas about convergence of series of functions are relegated to the appendix. That said, I learned many things from Edwards and I do think it is a great place to start.

The Dover text by Rosenlicht is a good analysis supplement to Edwards. Easy to read and it'll help you level-up analytically without much distraction.

If you want something lower level, take a look at Susan Colley's Vector Calculus, the first or 2nd ed. The text by Sternberg has tons of problems also. James Calahan wrote a beautiful text a few years ago, it's missing some generality, but the study of the interplay between linear algebra and implicit function theory is very pretty and I hope it finds a way into all the next generation advanced texts. It also makes some effort to explain the rudiments of Morse theory which is a bit unusual in a good way. A Differential Forms Approach Besides its engaging writing style, the solutions or at least good hints to every exercise in the book are given at the end of the book about 40 pages of carefully written solutions.

A recent book titled "Functions of several real variables" has many examples and solved problems that illustrate all notions and theorems. Its treatment of the subject is rigorous and its style modern and inviting. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered.

That should be more then enough to get you started-good luck! IgNite 1 Cook Dec 25 '12 at James Beats ne-but seems to happen a lot when I post and whoever it is is too cowardly to admit it. I think it's not a single person. Pavel did not ask the question; nargles did. I'll definitely look at Spivak's two texts.

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Cook 13k 2 28 Interestingly, no one has suggested the excellent and I had thought well known book Harold M. Edwards is wonderful,but it seriously needs to be updated in its treatment of linear algebra; he uses linear equations instead of matricies to present it. Why Edwards didn't take the opportunity to do that when the book was reissued and he corrected it is beyond me.

## Advanced Calculus of Several Variables

Mathemagician in my experience it was a fun exercise trying to "update" the linear algebra in the book. Makes you appreciate how useful matrices are when trying to work out the linear equations: Katherine sideri 41 1. Text and Readings in Mathematics Hindustan Book Agency If you were not in last semester, you might consider getting the first volume Analysis I. They are both exceptionally well priced. Here you will find the first four chapter of Tao's book in pdf format pdf file. There are many other excellent introductory analysis books.

Reading from other sources is always very valuable.

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I recommend two other books: There are 2 lectures per week. The course will cover Chapters 11 through 17 in Tao's books last chapter on Riemann integration in Book I , and time permitting we will say something about measures and Lebesgue integration in Rn Chapters and how it compares to Riemann integration.

This is the second part of a first one year course in analysis, concerned mostly about analysis on metric spaces, particularly analysis on several variables. We spent a good amount of time learning and practicing logical thinking. At this point I expect the students to have acquired the basic skills of mathematical reasoning, a deeper understanding of calculus, and to be ready to continue learning more analysis. Next topic of discussion will be metric spaces and point set topology, in particular the concepts of convergence of sequences, compactness, continuity and limits are revisited on metric spaces.

Emphasis in the notion of uniform convergence will be made, and its crucial role in interchanging limit operations: