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Mat-F March 16, 2005 Curvi-linear Coordinates, 10.10

Mat-F March 16, 2005 Curvi-linear Coordinates, 10.10. Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne. Overview. Sections 10.6-10.10 10.6 Scalar and vector fields scalar or vector that varies in space 10.7 Vector operators

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Mat-F March 16, 2005 Curvi-linear Coordinates, 10.10

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  1. Mat-FMarch 16, 2005Curvi-linear Coordinates, 10.10 Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne

  2. Overview • Sections 10.6-10.10 • 10.6 Scalar and vector fields • scalar or vector that varies in space • 10.7 Vector operators • gradient, divergence, curl • 10.8 Vector operator formulae • learn the magic! • 10.9 Vector operators in polar coordinates • explains what was used before • 10.10 General curvilinear coordinates • generalizes e.g. polars; Einsteins theory of general rel.

  3. Black board & Maple illustrations • Integral definitions of grad, div, and curl • Preview of Eqs. (11.14-11.16) page 404! • Preview of what line, surface, and volume integrals mean! • Beautiful; independent of coordinate systems! • Check that it means the same in Cartesian • Derive now easily the expressions in curvi-linear • Table 10.4, page 375b • Geometric interpretation • Visual / conceptual understanding!!!

  4. Enough for today! Good luck with the Exercises!

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