#### 1.1 Distance in Space

In this section we create the distance formula in space and apply it to spheres.

#### 1.2 Vectors in the Plane

In this section we define vectors in two dimensions and study their algebraic and geometric properties.

#### 1.3 Vectors in Space

In this section we define vectors in three dimensions and study their algebraic and geometric properties.

#### 1.4 The Dot Product

In this section we define the dot product and we use it to find the angle between vectors.

#### 1.5 The Cross Product

In this section we define the cross product and we use it to create orthogonal vectors.

#### 1.6 Lines in Space

In this section we describe lines in space analytically.

#### 1.7 Planes in Space

In this section we describe planes in space analytically.

#### 1.8 Cylinders and Quadric Surfaces

In this section we discover cylinders and quadric surfaces in $\R ^3$.

#### 2.1 Space Curves

In this section we create the describe curves in space.

#### 2.2 Calculus of Space Curves

In this section we define limits, derivatives and integrals of vector-valued functions.

#### 2.3 Differentiation Rules

In this section we will derive differentiation rules for vector-valued functions.

#### 2.4 Arc Length

In this section we compute arc length and we define the arc length parameter.

#### 2.5 Curvature

In this section we compute the curvature of a space curve.

#### 2.6 TNB Frames

In this section we determine the unit Normal and Binormal vectors.

#### 3.1 Functions of Several Variables

In this section we describe functions of two or more variables.

#### 3.2 Limits and Continuity

In this section we compute limits and define continuity.

#### 3.3 Partial Derivatives

In this section we define and compute partial derivatives.

In this section we compute the gradient vector and directional derivatives.

#### 3.5 Tangent Planes

In this section we determine tangent planes to surfaces.

#### 3.6 Chain Rule

In this section we compute partial derivatives using the chain rule.

#### 3.7 Maxima and Minima

In this section we determine local maxima and minima of a surface.

#### 3.8 Lagrange Multipliers

In this section we use Lagrange multipliers to find absolute maxima and minima.

#### 4.1 Double Integrals

In this section we define the double integral over a rectangle.

#### 4.2 More Double Integrals

In this section we compute double integrals over various regions.

#### 4.3 Polar Integrals

In this section we compute double integrals using polar coordinates.

#### 4.4 Triple Integrals

In this section we compute triple integrals over various regions.

#### 4.5 Cylindrical and Spherical Coordinates

In this section we compute triple integrals using cylindrical and spherical coordinates.

#### 4.6 Line Integrals and Work

We compute integrals of vector-valued functions along curves.