E0 · Vector calculus & foundations
A 22-module path through e0 · vector calculus & foundations, in study order from foundations to the frontier.
Modules
- Scalar and Vector Fields
- The Gradient Operator
- The Del Operator (Nabla)
- The Divergence of a Vector Field
- The Curl of a Vector Field
- Second Derivatives and the Laplacian
- Line Integrals
- Surface Integrals and Flux
- Volume Integrals
- The Fundamental Theorem for Gradients
- The Divergence (Gauss) Theorem
- The Curl (Stokes) Theorem
- Spherical Coordinates
- Cylindrical Coordinates
- Curvilinear Coordinates and Scale Factors
- The Dirac Delta Function in One Dimension
- The Three-Dimensional Dirac Delta Function
- The Helmholtz Theorem
- Scalar Potentials
- Vector Potentials
- Helmholtz Decomposition of Vector Fields
- Vector Identities and Product Rules