Talk:Calculus/Vector calculus

Proposed Chapter Layout
This chapter is designed to consolidate material related to vector calculus, in order address the length of chapter Calculus/Multivariable_calculus. This chapter will focus on the calculus that involves scalar and vector fields, and unlike chapter Calculus/Multivariable_calculus, will not focus on multi-variable calculus in general. The basic proposed structure of this chapter will be:

A brief discussion of scalar and vector fields.

A brief discussion of path, surface, and volume integrals with an emphasis on their respective infinitesimals/differentials.

A discussion of the gradient which includes: the fundamental theorem of calculus for path integrals; a derivation of the gradient for cylindrical and spherical coordinates; and a derivation of directional derivatives for cylindrical and spherical coordinates.

A discussion of the divergence which includes: Gauss' divergence theorem; and a derivation of the divergence for cylindrical and spherical coordinates.

A discussion of the Laplacian operator and a derivation of the Laplacian for cylindrical and spherical coordinates.

Lastly, a discussion of the curl which includes: Stoke's curl theorem; and a derivation of the curl for cylindrical and spherical coordinates.

The fundamental theorem of vector calculus, aka. Helmholtz decomposition, will be presented in a subsequent chapter after Green's function approaches to inverting the gradient, divergence, and curl are discussed.

Math buff (discuss • contribs) 21:35, 16 February 2017 (UTC)