Difference between revisions of "Multivariable calculus"

Latest revision as of 20:18, July 29, 2016

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

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 *[[Calc3.1]]
-[[Category:Vector analysis]]
+[[Category:Vector Analysis]]
 [[Category:Calculus]]
 [[Category:Mathematics]]