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