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  • Multivariable Calculus
  • Parametric Equations
  • Conic Sections
  • Vectors
  • Curves and Surfaces
  • Partial Differentiation
  • Gradients and Optimization
  • Multiple Integration
  • Vector Analysis

Multivariable Calculus

Author:
Kristen Beck
Topic:
Calculus, Vectors
Multivariable Calculus

Table of Contents

  • Parametric Equations

    • Parametric Equations
    • Different Parameterizations
    • Parameterizing an Ellipse
    • Curves in 2-Space
    • Curves in 3-Space
    • Tangent Line to a Parametric Curve
    • Regions Bounded by Polar Curves
  • Conic Sections

    • The Foci of an Ellipse
    • The Foci of a Hyperbola
    • The Focus and Directrix of a Parabola
  • Vectors

    • Sum/Difference of Vectors
    • Parametric Representation of a Line
    • Vector Representation of a Line
    • Intersecting Lines
    • Geometric Interpretation of the Dot Product
    • Orthogonal Projection
    • Geometric Interpretation of the Cross Product
  • Curves and Surfaces

    • Level Curves
    • Cylindrical Coordinates
    • Spherical Coordinates
    • Curve Along a Surface
  • Partial Differentiation

    • Partial Derivatives and Slope
    • The Chain Rule
    • Tangent Plane to a Surface
  • Gradients and Optimization

    • Gradient vs. Level Curves
    • Constrained Optimization
  • Multiple Integration

    • Small Cylindrical Volumes
    • Small Spherical Volumes
    • Iterated Double Integrals
    • Line Integral of a Scalar Function
    • Simple Cylindrical Volumes
    • Simple Spherical Volumes
  • Vector Analysis

    • Vector Field in the Plane
    • Line Integral of a Vector Field in 2-Space
    • Line Integral of a Vector Field in 3-Space
    • Circulation in 2-Space
Next
Parametric Equations

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