| Title; Textbook Sections |
Hours
(Approx) |
Description |
Coordinate Geometry in Space
10.1-10.4
|
3 |
- Analytic geometry in 2- and 3-space
- Vectors, dot products, projections
- Cross products
- Planes and lines
|
Vector-Valued Functions of One Variable
11.1-11.3
|
3 |
- Derivatives
- Interpretations: velocity, speed, acceleration
- Parametrizing curves
|
Scalar Fields
10.5; 12.1-12.9
|
9 |
- Visualization
- Partial derivatives
- Linear approximations
- Gradients and directional derivatives
- Higher order derivatives
- Quadratic approximations
- Chain rule and implicit functions
|
Using Partial Derivatives
13.1-13.3, 13.6
|
5 |
- Local maxima and minima
- Constrained optimization
- Newton's method
|
Multiple Integrals
14.1-14.6
|
8 |
- Double integrals; iteration and re-iteration
- Polar coordinates
- Triple integrals
- Cylindrical and spherical coordinates
|
Vector Fields
15.1-15.6
|
8 |
- Visualization
- Line integrals
- Conservative fields and potentials
- Surfaces in 3-space:
parametric form, graph form, level-set form
- Integrals of scalar functions over surfaces in 3-space
- Oriented surfaces and flux integrals
|
Vector Calculus, with Applications
16.1-16.6
|
9 |
- Divergence, gradient, and curl; identities
- Vector potentials
- Theorems of Gauss, Green, and Stokes
- Applications to conservation laws, fluid flow, electrostatics
|
| Hours on Outline
|
45 |
- (50 meetings this term, 3 used for tests.)
|