Good resources for integrals in Four-Space?

[Master J]

I've been looking for some good resources on integrals in four-space (SR and GR), and hope someone can suggest some! I'm not too interested in abstract mathematical formalisms to the extent of pure math though, I must keep in mind that this is all to do with physics (at least for me!).

I know there are 4 kinds of integrals one can do in four-space:

(1) Integrate a line element, ie. a curve.
(2) Surface integral on a 2-D surface.
(3) Integral on a 3-D hypersurface.
(4) 4-D volume integral.

Landau-Lifgarbagez gives a brief intro in their field theory book but I'd like to clear some things up instead of just having formulae presented to me.

Any suggestions?

Cheers guys!

 

[Master J]

Could anyone even tell me what area of math these fall under? Including such things as generalizations of Stokes and Gauss' theorems to hifger dimensions.

 

[Ben Niehoff]

You should read about differential forms, but you have voiced a non-interest in "mathematical formalism", so you may well be stuck.

 

[George Jones]

For general relativity, I think some of what you want is in sections 3.1, 3.2, and 3.3 from Eric Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of black hole Mechanics.