# Differential Forms: High Level Approach to Real Analysis?

I am currently skimming through the differential forms book by Edwards. I was wondering whether real analysis is basically just a special case of differential forms? I am learning about flows, 1-forms, 2-forms, Fundamental Theorem of Calculus, etc...

These seem to be analogous to the topics in a typical real analysis course. So is the differential forms approach just a high level approach to real analysis? Would I appreciate real analysis more if I first go through differential forms? It seems to illuminate the machinery behind multivariable calculus.

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Real Analysis$\neq$Multivariate Calculus –  Michael Greinecker Feb 8 '12 at 18:54
Differential forms help you sort out the later stuff in calc 3 -- Green's Theorem, Stokes Theorem, etc. You can use them to do differential equations, but they can't tell you, for example, when a differential equation has a solution -- for that you will need analysis. They are really just "nice algebraic structures" that from time to time are very useful. –  tomcuchta Feb 8 '12 at 19:01
To summarize: Differential forms provide a high-level approach to vector calculus (in multivariable calculus). However, there is more to real analysis than just vector calculus. –  Jesse Madnick Feb 8 '12 at 19:23

You might want to consider Shlomo Sternberg's Advanced Calculus. It's freely available online:

Harvard: Books of Shlomo Sternberg

Though the primary approach in that book isn't based on differential forms, if you're looking for a "high level" approach to real analysis, the book can prove very useful.

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