1. Saturday Sept 19th: Vector Calculus Vector derivatives of a scalar field: gradient, directional derivative, Laplacian Vector derivatives of a vector field: divergence, curl

2. Scalar fields unit vectors e.g. temperature oxygen content

3. e.g. surface pressure = P(longitude, latitude)

4. Differentiating a scalar: directional derivative, gradient gradient directional derivative

5. Pressure gradient

6. Pressure gradient force

8. Examples

9. A vector differential operator “Del”, or “Nabla”,

10. The Laplacian

11. 2,3 dimensional PDEs Laplace’s eq’n Diffusion eq’n Wave eq’n

12. Vector fields

13. Differentiating a vector field examples

14. Divergence of a vector field

15. Modeling rain

16. Curl

17. Example: river flow

18. Diffusion (friction) Concentration of velocity diffuses away

19. Example: river flow gravity

20. Example: river flow

21. curl

22. Identities of vector calculus