# Multivariable calculus

**Multivariable calculus** is a college-level topic of study that typically includes:

- Vector space
- equations of planes, finding lines perpendicular to planes
- dot product
- cross product

- Arc length, area and volume
- recognizing shapes of different functions
- area between curves
- volume of intersecting solids
- disk, circular ring and cylindrical shell formulas

- Vector fields
- gradient
- divergence
- curl
- line integral
- conservative field
- defined by line integral, contour integral, curl, and gradient

- surface integral
- isolating singularities

- Green's Theorem
- solving integrals split into separate expressions for
*dx*and*dy* - finding area enclosed by a contour

- solving integrals split into separate expressions for
- Stoke's Theorem
- solving contour integrals when curl over capping surface can be found, and vice-versa

- Divergence Theorem
- solving volume integrals for divergence when enclosing surface integral can be found, and vice-versa

- multiple integrals
- substitution
- curvilinear coordinates

- Maxima
- with constraints (Lagrangian multiplier and Hessian)
- parametrization
- related rates (e.g., filling volumes)

- continuity
- limits
- differentiability
- L'Hopital's Rule
- partial derivatives
- Jacobian

- Power series