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
  - parameterization
- 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
- 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
- Taylor series

See also