Table of Contents

1. Parametric Equations
   1. Parametric Equations
   2. Different Parameterizations
   3. Parameterizing an Ellipse
   4. Curves in 2-Space
   5. Curves in 3-Space
   6. Tangent Line to a Parametric Curve
   7. Regions Bounded by Polar Curves
2. Conic Sections
   1. The Foci of an Ellipse
   2. The Foci of a Hyperbola
   3. The Focus and Directrix of a Parabola
3. Vectors
   1. Sum/Difference of Vectors
   2. Parametric Representation of a Line
   3. Vector Representation of a Line
   4. Intersecting Lines
   5. Geometric Interpretation of the Dot Product
   6. Orthogonal Projection
   7. Geometric Interpretation of the Cross Product
4. Curves and Surfaces
   1. Level Curves
   2. Cylindrical Coordinates
   3. Spherical Coordinates
   4. Curve Along a Surface
5. Partial Differentiation
   1. Partial Derivatives and Slope
   2. The Chain Rule
   3. Tangent Plane to a Surface
6. Gradients and Optimization
   1. Gradient vs. Level Curves
   2. Constrained Optimization
7. Multiple Integration
   1. Small Cylindrical Volumes
   2. Small Spherical Volumes
   3. Iterated Double Integrals
   4. Line Integral of a Scalar Function
   5. Simple Cylindrical Volumes
   6. Simple Spherical Volumes
8. Vector Analysis
   1. Vector Field in the Plane
   2. Line Integral of a Vector Field in 2-Space
   3. Line Integral of a Vector Field in 3-Space
   4. Circulation in 2-Space