Math2111: Chapter 5: Additional Material: Differential forms and the general Stokes’ theorem

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

We have studied a variety of generalisations of the fundamental theorem of calculus:

• the fundamental theorem of line integrals;
• Green’s theorem;
• Stokes’ theorem;
• Gauss’ Divergence theorem;

Now we show how all of these formulae concisely fit into one approach. Differential forms provide the underlying theory to present all formulae in one framework. This also allows us to generalise the theorems above to arbitrary dimensions.