| SECTION |
CONCEPTS |
METHODS |
| 16.1 The Definite Integral of a Function of Two Variables |
- Riemann sums in a double variable situation
- Double integral as volume
- Double integral as area
|
- Describing regions in the plane
|
| 16.2 Iterated Integrals |
|
- Calculating a "partial integral"
- Reversing the order of integration
|
| 16.3 Triple Integrals |
- Volume as a triple integral
|
- Describing regions in three-space
- Evaluating triple integrals
|
| 17.1 Parameterized Curves |
|
- Writing parametric equations for a line
- Writing a vector equation for a line
- Intersections of lines and surfaces
|
| 17.2 Motion, Velocity, and Acceleration |
- How these concepts are related through derivatives
- The velocity vector is tangent to the curve
- Speed and velocity
|
- Calculating derivatives of vector functions
- Finding tangent lines to a curve
- Calculating arc length by an integral
|
| 17.3 Vector Fields |
- Definition as a function
- Visualizing by a graph
|
- Using a gradient to create a vector field
|