MP0 · Vector calculus & integral theorems
A 25-module path through mp0 · vector calculus & integral theorems, in study order from foundations to the frontier.
Modules
- Scalar and Vector Fields
- The Gradient Operator
- Directional Derivative
- Divergence of a Vector Field
- Curl of a Vector Field
- The Del Operator and Vector Differential Identities
- The Laplacian Operator
- Line Integrals
- Surface Integrals and Flux
- Volume Integrals
- The Divergence (Gauss) Theorem
- Stokes' Theorem
- Green's Theorem in the Plane
- Green's Identities
- Conservative Fields and Scalar Potentials
- Solenoidal Fields and Vector Potentials
- Helmholtz Decomposition Theorem
- Orthogonal Curvilinear Coordinates
- Scale Factors and Line, Area and Volume Elements
- Cylindrical Polar Coordinates
- Spherical Polar Coordinates
- Vector Operators in Curvilinear Coordinates
- The Jacobian and Change of Variables
- Index Notation and the Summation Convention
- The Kronecker Delta and Levi-Civita Symbol