saturday sept 19th vector calculus n.
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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

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
Scalar fields

unit

vectors

e.g. temperature

oxygen content

a vector differential operator
A vector differential operator

“Del”, or “Nabla”,

2 3 dimensional pdes
2,3 dimensional PDEs

Laplace’s eq’n

Diffusion eq’n

Wave eq’n

example river flow1
Example: river flow

Diffusion

(friction)

Concentration of

velocity diffuses away