Course, Calculus, Math, Jenn Stulls, Multivariable Calculus

What is Calculus 3?

The following video provides an outline of all the topics you would expect to see in a typical Multivariable Calculus class (i.e., Calculus 3, Vector Calculus, Multivariate Calculus).

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Vectors and The Geometry of Space

7 Videos  36 Examples

  • Three-Dimensional Coordinate Systems
  • Vectors
  • The Dot Product
  • The Cross Product
  • Equations of Lines and Planes
  • Cylinders and Quadric Surfaces
  • Cylindrical and Spherical Coordinates

Vector Functions

5 Videos  28 Examples

  • Vector Functions and Space Curves
  • Derivatives and Integrals of Vector Functions
  • Unit Tangent Vectors
  • Arc Length and Curvature
  • Motion in Space: Velocity and Acceleration

Partial Derivatives

8 Videos  63 Examples

  • Functions of Several Variables
  • Limits and Continuity
  • Partial Derivatives
  • Tangent Planes and Linear Approximations
  • The Chain Rule for Functions of Several Variables
  • Directional Derivatives and the Gradient Vector
  • Maximums and Minimum Values for Functions of Several Variables
  • Lagrange Multipliers

Multiple Integrals

9 Videos  48 Examples

  • Double Integrals over Rectangles
  • Iterated Integrals
  • Double Integrals over General Regions
  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals: Density, Mass and Moments of Inertia
  • Surface Area
  • Triple Integrals
  • Triple Integrals in Cylindrical and Spherical Coordinates
  • Change of Variables in Multiple Integrals

Vector Calculus

9 Videos  58 Examples

  • Vector Fields
  • Line Integrals
  • The Fundamental Theorem of Line Integrals
  • Green’s Theorem
  • Curl and Divergence
  • Parametric Surfaces and Their Areas
  • Surface Integrals
  • Stoke’s Theorem
  • The Divergence Theorem

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