1. Mat-F March 14, 2005 Vector Calculus, 10.6-10.10 Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne

2. 10: Vector operators Why? Because most laws of physics derived this way conservation laws electrodynamics … How? Generalization of chain rule for derivatives Lots of examples on the black board!

3. 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.

4. Black board 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.

5. Black board 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.

6. Black board 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.

7. Black board 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.

8. Black board 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.

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