Function graphs; parametric curves.
Vector calculus is about differentiation and integration of vector fields. This article gives an overview of the differentiation. operations.
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Find the volume between a function f(x,y) and a certain region in the xy-plane.
Line integrals in scalar field; line integrals in vector field;.
When a vector field is a gradient of function f(x,y), it is called a gradient field.
For a velocity field, curl measures the rotation component of the motion. Curl also measures how far the vector field is from being conservative.
Flux is the amount of something (water, wind, electric field, magnetic field) passing through a surface.