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# Mat-F March 16, 2005 Curvi-linear Coordinates, 10.10 - PowerPoint PPT Presentation

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-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

• 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.

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!!!

• Good luck with the Exercises!