Vectors and the Geometry of Space

3D Coordinate System (Scott Surgent, 15:05)
• Sphere Example 1 (Richard Ruedemann, 2:44)
• Sphere Example 2 (Richard Ruedemann, 2:21)
• Notes: R^3, points, distance formula, spheres, surfaces
• Typed Examples: Points, distances, spheres in R^3

Vectors (Scott Surgent, 12:55)
• Vector Magnitude Example (Richard Ruedemann, 2:19)
• Vector Addition Example (Richard Ruedemann, 3:21)
• Notes: Hints for the hanging mass problem
• Notes: Vectors
• Typed Examples: Vectors

The Dot Product (Scott Surgent, 15:18)
• Angle Between Vectors Example (Richard Ruedemann, 3:09)
• Vector Projection Example (Richard Ruedemann, 4:26)
• Decomposing Vectors Using Projections Example (Richard Ruedemann, 4:02)
• Notes: The "One Right-Angle Turn" Problem
• Notes: Dot Product
• Typed Examples: Dot Product

The Cross Product (Scott Surgent, 13:59)
• Triangle Area Example (Richard Ruedemann, 3:37)
• Typed Examples: Vectors, Dot Product and Projections, Cross Product and Scalar Triple Products
• Notes: Cross Product
• Notes: Proof of the Magnitude of a Cross Product

Equations of Lines and Planes - Part 1 (Scott Surgent, 10:51)
Equations of Lines and Planes - Part 2 (Scott Surgent, 12:40)
• Parameterizing a Line Segment (Richard Ruedemann, 3:32)
• Intersection of Two Lines (Richard Ruedemann, 6:50)
• Distance from a Point to a Line (Richard Ruedemann, 4:45)
• Angle between Planes (Richard Ruedemann, 3:26)
• Notes: Lines & Planes in R^3
• Typed Examples: Cross Product and Scalar Triple Products
• Typed Examples: Lines in R^3
• Typed Examples: Planes in R^3

Cylinders and Quadratic Surfaces (Scott Surgent, 17:43)
• Equation of an Ellipsoid (Richard Ruedemann, 2:11)
• Intersection of a Paraboloid and a Plane (Richard Ruedemann, 4:42)
• Typed Examples: Multivariable Functions and Traces in x, y, and z

Vector Functions and Spacecurves (Scott Surgent, 17:33)
• error correction for the above video
• Notes: Vector-Valued Functions
• Typed Examples: Vector-Valued Functions with Differentiation, Arc Length, Unit Tangent, Unit Normal Vectors

Arc Length (Scott Surgent, 11:09)
• Arc Length Example (Richard Ruedemann, 3:37)
• Arc Length Example 2 (Richard Ruedemann, 3:53)
• Vector-Valued Integration (Richard Ruedemann, 4:25)
• Notes: Vector-Valued Functions
• Typed Examples: Vector-Valued Functions with Differentiation, Arc Length, Unit Tangent, Unit Normal Vectors

Motion in Space: Velocity and Acceleration (Scott Surgent, 12:33)
• Minimum Speed Example (Richard Ruedemann, 2:55)
• Notes: Unit Tangent, Unit Normal, ds segmentation
• Notes: More on T, N, and the ds and dt segmentation
• Typed Examples: Projectile Motion

Partial Derivatives and Applications

Functions of Several Variables (Scott Surgent, 17:26)
• error correction for the above video
• Contour Maps Example (Richard Ruedemann, 2:21)
• Contour Map through a Specific Point Example (Richard Ruedemann, 0:50)
• Notes: Multi-var Functions, Domain, Range
• Typed Examples: Level Curves & Contour Maps

Partial Derivatives (Scott Surgent, 11:31)
• Partial Derivative Example (Richard Ruedemann, 3:58)
• Implicit Partial Derivative Example (Richard Ruedemann, 3:28)
• Notes: Partial Derivatives
• Typed Examples: Partial Derivatives

Tangent Planes and Linear Approximations (Scott Surgent, 13:22)
• Estimating Function Values Example (Richard Ruedemann, 3:02)
• Change in Volume Example (Richard Ruedemann, 2:48)
• Typed Examples: Tangent Planes and Linear Approximations

The Chain Rule (Scott Surgent, 18:23)
• Notes: 2nd derivatives, tangent planes, the chain rule, directional derivatives
• Typed Examples: The Chain Rule

Gradient and Directional Derivatives (Scott Surgent, 22:25)
• Directional Derivative Example (Richard Ruedemann, 2:38)
• Notes: tangent planes, differentials, directional derivatives
• Typed Examples: Directional Derivatives & the Gradient

Maximum and Minimum Values (Scott Surgent, 14:39)
• Critical Points Example (Richard Ruedemann, 4:05)
• Classifying the above CP's Example (Richard Ruedemann, 4:20)
• Typed Examples: Unconstrained Optimization (local extrema)
• Typed Examples: Constrained Optimization (absolute extrema)

Multiple Integrals

Double Integrals Over Rectangles (Scott Surgent, 13:50)
• error correction for the above video
• Notes: Multi-var Integration
• Typed Examples: Riemann Sums and Integration over Rectangles

Double Integrals over General Regions (Scott Surgent, 18:12)
• Reversing the Order of Integration to Evaluate Example1 (Richard Ruedemann, 3:17)
• Reversing the Order of Integration to Evaluate Example2 (Richard Ruedemann, 3:04)
• Reversing the Order of Integration to Evaluate Example3 (Richard Ruedemann, 4:16)
• Notes: More Multi-var Integration
• Typed Examples: Double Integrals over type I regions
• Typed Examples: Double Integrals over type II regions

Double Integrals in Polar Coordinates (Scott Surgent, 15:54)
• Polar Integration Example (Richard Ruedemann, 6:37)
• Notes: Polar, Centers of Mass
• Typed Examples: Polar Coordinates

Triple Integrals (Scott Surgent, 19:09)
• 6 way Integration Example (Richard Ruedemann, 14:20)
• Notes: Triple Integrals
• Typed Examples: Triple Integrals & Cylindrical Coordinates

Triple Integrals in Cylindrical Coordinates (Scott Surgent, 13:28)
• Typed Examples: Triple Integrals & Cylindrical Coordinates

Triple Integrals in Cylindrical Coordinates (Scott Surgent, 17:07)
• Notes: Spherical Coordinates
• Typed Examples: Spherical Coordinates

Vector Calculus

Vector Fields (Scott Surgent, 16:03)
• Notes: Vector Fields
• Typed Examples: Vector Fields

Line Integrals part 1 (Scott Surgent, 11:23)
Line Integrals part 2 (Scott Surgent, 16:23)
• Line Integral Example (Richard Ruedemann, 14:20)
• Notes: Line Integrals
• Typed Examples: Line Integrals
• Optional: Flux Line Integrals

Fundamental Theorem of Line Integrals (Scott Surgent, 20:59)
• Potential Example (Richard Ruedemann, 3:37)
• Notes: Path Independence, Fundamental Theorem of Line Integrals
• Typed Examples: Conservative Vector Fields and The Gradient, The Fundamental Theorem of Line Integrals

Green's Theorem (Scott Surgent, 15:15)
• Notes: Green's Theorem
• Typed Examples: Green's Theorem

Curl and Divergence (Scott Surgent, 14:48)
• Curl Example (Richard Ruedemann, 4:54)
• Typed Examples: Del Operator: Curl and Divergence

Parametric Surfaces and their Areas - part 1 (Scott Surgent, 10:21)
Parametric Surfaces and their Areas - part 2 (Scott Surgent, 18:46)
• Typed Examples: Surface Area

Surface Integrals (Scott Surgent, 20:32)
• error correction for the above video
• Typed Examples: Surface Integrals
• Typed Examples: Flux Through Solids; Divergence Theorem