1. Mat-F March 16, 2005 Curvi-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!