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Saturday Sept 19th: Vector Calculus

Saturday Sept 19th: Vector Calculus. Vector derivatives of a scalar field : gradient, directional derivative, Laplacian Vector derivatives of a vector field : divergence, curl. Scalar fields. unit vectors. e.g. temperature oxygen content.

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Saturday Sept 19th: Vector Calculus

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  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 directional derivative gradient

  5. Pressure gradient

  6. Pressure gradient force

  7. 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. Example: river flow Diffusion (friction) Concentration of velocity diffuses away

  19. Example: river flow gravity

  20. Example: river flow

  21. Example: river flow curl

  22. Identities of vector calculus

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