Multivariable Calculus Tags

Multivariable Calculus Tags

Vector geometry

  • Vectors and vector arithmetic
  • Dot product, length, and unit vectors
  • Cross product
  • Coordinate systems

Calculus of vector valued functions

  • Parameterized curves
  • Limits and continuity
  • Derivatives
  • Integrals
  • Arc length and curvature
  • Frames, motions, and other applications

Concepts for multivariable functions

  • Notation, domain, and range
  • Surfaces
  • Quadratic surfaces
  • Surfaces in other coordinate systems
  • Parameterized surfaces
  • Traces, contours, and level sets

Differentiation of multivariable functions

  • Limits and continuity
  • Partial derivatives
  • Chain rule
  • Differentiability, linearization and tangent planes
  • Directional derivatives and the gradient
  • Extreme values and optimization
  • Lagrange multipliers and constrained optimization

Integration of multivariable functions

  • Double integrals over rectangles
  • Iterated integrals and Fubini's theorem
  • Double integrals over general regions
  • Double integrals in polar
  • Triple integrals
  • Change of variable
  • Triple integrals in cylindrical and spherical
  • Applications of double integrals
  • Applications of triple integrals

Vector fields

  • Graphs, flows lines, and level surfaces
  • Identifying extrema from graphs

Vector calculus

  • Derivatives
  • Line integrals
  • Conservative vector fields
  • Applications of line integrals
  • Curl and divergence
  • Surface integrals of scalar fields
  • Surface integrals of vector fields

Fundamental theorems

  • Line integrals
  • Green's theorem
  • Stokes' theorem
  • Divergence theorem
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License