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

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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

Overview
• 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!!!
Enough for today!

Good luck with the Exercises!