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[edit]

• Calc3.1