Good resources for integrals in Four-Space?

In summary, the person is looking for resources on integrals in four-space for use in physics. They are not interested in purely mathematical formalisms and are specifically seeking resources that explain the concepts rather than just presenting formulas. They mention four types of integrals that can be done in four-space and ask for suggestions on where to find more information. They also mention the area of math that these integrals fall under and suggest reading about differential forms, but acknowledge that their lack of interest in mathematical formalism may make it difficult to understand. They also recommend checking out Eric Poisson's notes and book for more information on general relativity and black hole mechanics.
  • #1
Master J
226
0
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!
 
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  • #2
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.
 
  • #3
You should read about differential forms, but you have voiced a non-interest in "mathematical formalism", so you may well be stuck.
 
  • #4
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.
 

Related to Good resources for integrals in Four-Space?

1. What is Four-Space?

Four-Space, also known as four-dimensional space, is a mathematical concept that extends the traditional three dimensions of length, width, and height into a fourth dimension. It is often used in advanced calculus and physics to represent complex systems and phenomena.

2. Why are integrals in Four-Space important?

Integrals in Four-Space are important because they allow us to calculate the volume, surface area, and other properties of objects and systems in four-dimensional space. This is crucial in fields such as physics, engineering, and computer graphics.

3. What are some good resources for learning about integrals in Four-Space?

There are many resources available for learning about integrals in Four-Space, including textbooks, online courses, and videos. Some recommended resources include "Calculus on Manifolds" by Michael Spivak, "Advanced Engineering Mathematics" by Erwin Kreyszig, and the "Multivariable Calculus" course on Khan Academy.

4. Are there any specific techniques for solving integrals in Four-Space?

Yes, there are several techniques for solving integrals in Four-Space, including the change of variables method, integration by parts, and using symmetry and trigonometric identities. It is important to have a good understanding of these techniques and how they apply in four-dimensional space.

5. How can I practice and improve my skills in solving integrals in Four-Space?

One of the best ways to practice and improve your skills in solving integrals in Four-Space is to solve a variety of practice problems. Many textbooks and online resources offer a range of problems with solutions for you to work on. Additionally, working with a study group or seeking help from a tutor can also be beneficial.

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