Recent content by Bill2500

It does not add it to my post. Why?

I don't know how I can upload a picture so I found a link of the book and included it.

Thank you very much for your extensive reply!

I am studying Analysis on Manifolds by Munkres. He introduces improper/extended integrals over open set the following way: Let A be an open set in R^n; let f : A -> R be a continuous function. If f is non-negative on A, we define the (extended) integral of f over A, as the supremum of all the...

Where is topology useful in physics? I show some sections of Spivak's Differential Geometry book and Munkres' complicated proofs and it seemed topology is a really useful mathematical TOOL for other things. My problem is that I am probably going to specialize in particle physics, quantum theory...

Hello. I am studying Analysis on Manifolds by Munkres. My aim is to be able to study by myself Spivak's Differential Geometry books. The problems is that the proof in Analysis on Manifolds seem many times difficult to understand and I am having SERIOUS trouble picturing myself coming up with...

I thought boundedness is something I can claim for a range if I have fa compact domain.

I have had a course in one variable at a level a bit higher than Spivak and a (slightly less rigorous) course in multivariable course. I am studying this book to proceed to Spivak's Differential Geometry books but I am having second thoughts. Seeing how much topology Munkres' proofs have I am...

Hello. I am studying Analysis on Manifolds by Munkres. I have a problem with a proof in section 20. It states that: Let A be an n by n matrix. Let h:R^n->R^n be the linear transformation h(x)=A x. Let S be a rectifiable set (the boundary of S BdS has measure 0) in R^n. Then v(h(S))=|detA|v(S)...

Thank you anorlunda!

Hello. I am Bill. I am an undergraduate physics student. I am interested in the mathematics of the physical science. My aim is managing to make the physics fields I will be mostly interested in the future as mathematically rigorous, intuitive, geometrical and accesible as humanly possible. I...