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

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Mat-FMarch 16, 2005Curvi-linear Coordinates, 10.10

Åke Nordlund

Niels Obers, Sigfus Johnsen

Kristoffer Hauskov Andersen

Peter Browne Rønne

- 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.

- 10.6 Scalar and vector fields

- 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!

- Check that it means the same in Cartesian
- Derive now easily the expressions in curvi-linear
- Table 10.4, page 375b

- Visual / conceptual understanding!!!

Good luck with the Exercises!