**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**

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**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**