Recent content by gts87

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    Graduate Surface integral with differential forms

    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...
    • gts87
    • Thread
    • Differential Differential forms Forms Integral Surface Surface integral
    • Replies: 1
    • Forum: Differential Geometry
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    Undergrad Solving the Mystery of cos(2 theta) = 1 - 2sin^2(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.
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    Graduate Basis for tangent space and cotangent space

    Thanks, great explanation.
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    Graduate Is there a standard for the definition of the wedge product?

    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...
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    Graduate Basis for tangent space and cotangent space

    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...
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    Graduate A Geometric Approach to Differential Forms by David Bachman

    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}...