Hi, I'm trying to solve a problem in David Bachman's Geometric Approach to Differential Forms (teaching myself.) The problem is to integrate the scalar function f(x,y,z) = z^2 over the top half of the unit sphere centered at the origin, parameterized by \phi(r,\theta) = (rcos\theta, rsin\theta...
I would say first consider cos(2\theta) = cos(\theta + \theta), then use the sum to product formula cos(\alpha + \beta) = (cos\alpha)(cos\beta) - (sin\alpha)(sin\beta). See if you can go from there.
In Bachman's book (A Geometric Approach to Differential Forms) he describes the wedge product as a determinant. First he defines \omega\wedge\nu(V_{1},\;V_{2}) = det[\omega(V_{1})\;\omega(V_{2})\;\;,\;\;\nu(V_{1})\;\nu(V_{2})] (sorry about the formatting there -- the first and second rows of the...
Hello, I'm trying (somewhat haphazardly) to teach myself about differential forms. A question I have which is confusing me at the moment is about the tangent and cotangent spaces.
In https://www.physicsforums.com/showthread.php?t=2953" the basis for the tangent space was described in terms of...
Sorry, hate to dig up an old thread but I found it relevant to my question. I'm using this book to teach myself about differential forms and the generalized Stokes' theorem.
On page 32 (2006 edition) Bachman asks to evaluate the following integral:
\int_{R}...