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Vectors and The Geometry of Space
7 Videos 36 Examples
- Three-Dimensional Coordinate Systems
- The Dot Product
- The Cross Product
- Equations of Lines and Planes
- Cylinders and Quadric Surfaces
- Cylindrical and Spherical Coordinates
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
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
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
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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