Math 267 Lecture Videos
The Three-Dimensional Coordinate System
Geometric Representation of Vectors; Vector Sum, Scalar
Multiple, and Difference
Algebraic Representation of Vectors
Algebraic Representation of Vectors II
Examples and Applications of 2D Vectors
Properties of the Vector Product
Distance from a Point to a Line
Parallel and Orthogonal Planes
The Intersection of Two Planes
Differentiation Formulas and Finding Parametric Equations
of the Tangent Line
Integrating Vector-valued Functions
Necessary Condition for the Orthogonality
of the Position and Derivative Vectors
Projectile Motion: Parabolic Path
Projectile Motion: Initial and Final Speeds
Unit Tangent and Unit Normal Vectors
Arclength Parametrization Example
Formula for Curvature When the Cartesian Equation of a
Plane Curve is Given
Formula for Curvature When Parametric Equations of a
Plane Curve are Given
Tangential and Normal Components of Acceleration
Formulas for the Acceleration Components and Curvature
Involving Only the Derivatives of r(t)
Review of Vector-Valued Functions and Motion
Finding the Center of Curvature
Functions of Several Variables
Level Curves and Level Surfaces
Limit of a Function of Several Variables
Nick Explains the Definition of a Limit
Evaluating Limits of Multivariable Functions
Finding the Limit Using the Equations of the Lines of
Approach
Finding Limits for Functions of Three Variables Using
Parametric Equations of the Lines of Approach
Finding Limits Using Polar Coordinates
Continuity of Functions of Several Variables
Proof of the Epsilon Form of the Increment
Increment Epsilon Form: Another Example
Tangent Planes and Normal Lines
Example for the Direction of the Gradient
Local Extrema and Critical
Points
Tests for Local Extrema and
Saddle Points
Examples of Finding Extrema and
Saddle Points
Example of Critical Point Obtained from Undefined Partial
Derivative
Extrema over a Closed and Bounded Region
Example: Minimizing the Distance between Parallel Planes
An Optimization Problem: Constructing a Gutter
Setting Up Iterated Double Integrals
Areas and Volumes Using Double Integrals
Rx and Ry Regions Explained Again
More Examples of Finding Volumes
Double Integration in Polar Coordinates
Cartesian to Polar Integration
Volumes Using Polar Coordinates
Volumes Using Triple Integrals
Volumes and Centroids Using Cylindrical
Coordinates
Line Integral along Different Paths between Two Points
Mass and Center of Mass of a Wire
Application of the Line Integral to Force Fields
Necessary and Sufficient Condition for Independence of Path
Finding the Potential Function
Another Example of Finding the Potential Function
Another Necessary and Sufficient Condition for Independence
of Path
The Law of Conservation of Energy
Using Green’s Theorem to Find Areas
Vector Form of Green’s Theorem