Week

Sec.

Topic

Materials

Resources

1

12.1

Three dimensional coordinate systems

Calculus I and II Review

A robust 3D grapher

12.2

Vectors

Lengths of vectors

Seeing a vector in 3D

12.3

The dot product

The dot and cross products

The dot product in 3D

12.4

The cross product

Practice with vectors (optional)

Visualizing the cross product

2

12.5

Equations of lines and planes

Intersections of lines and planes

Parameterizing a line in 3D

12.6

Cylinders and quadric surfaces

Understanding surfaces

Visualzing quadric surfaces

3

14.1

Functions of several variables

Contour plots and multivariable domains

Bivariate functions in Desmos
A robust 3D grapher

14.3

Partial derivatives

Higherorder partials

Visualizing the partial derivative at a point

14.4

Tangent planes and linear approximation

Tangent planes and linearization

Seeing an infinite collection of tangent lines.
A "good" linear approximation.
Examples used in class:
#1 (.png)
#2 (.png)
#3 (.png)

14.5

The chain rule

The chain rule


4

14.6

Directional derivatives and the gradient vector

The gradient and directional derivatives

Visualizing directional derivatives

14.7

Local extrema of multivariate functions

Classifying extrema

Visualizing absolute and local extrema
A function with one local max, two local mins and three saddle points.
A hard function to graph with a local minimum

15.1

Double integrals over rectangles

Double integrals over rectangles

Visualizing a single and a double Riemann sum

5

15.2

Double integrals over general regions

Double integrals over general regions


15.3

Double integrals in polar coordinates

Double integrals in polar coordinates


6


Review




Exam 1:
7:30  8:30pm on 10/2
Covers sections 12.1  12.6, 14.1, 14.2, 14.3  14.7, 15.1  15.3

Practice Exam 1
(Solutions)
Review Exercises



Review of exam 1



15.3

Double integrals in polar coordinates



15.6

Triple integrals

Triple integrals


7

15.6

Triple integrals



15.7

Triple integrals in cylindrical coordinates

Triple integrals in cylindrical coordinates

Visualizing cylindrical coordinates

8

15.7

Triple integrals in cylindrical coordinates



15.8

Triple integrals in spherical coordinates

Triple integrals in spherical coordinates

Visualizing spherical coordinates
Basic surfaces in spherical coordinates




Triple integrals "cheatsheet"

13.1

Vector functions and space curves


Interactive examples
Space curves
#1
and
#2
A line segment
A gallery of space curves

9

13.2

Calculus of vectorvalued functions

Vector functions part 1


13.3

Arc length

Vector functions part 2

Visualizing approximations of arc length
A few practice problems

16.2

Line integrals of scalar functions

Line integrals of scalar functions

The area calculated in a line integral and in one projection

10

16.2 (and 16.1)

Line integrals of vector fields

Line integrals of vector fields

Vector field examples
#1
#2
and
#3

16.3

The fundamental theorem for line integrals

Fundamental theorem for line integrals


11

16.4

Green's theorem

Green's theorem



Review




Exam 2:
7:30  8:30pm on 11/8
Covers sections 15.4, 15.6  15.8, 13.1  13.3, 16.1  16.3

Practice Exam 2
(Solutions)
Review Exercises


12

16.5

Curl and divergence

Curl and Divergence

Curl examples
#1
#2
#3
#4
#5
Divergence examples

16.6

Parametric surfaces and their areas

Parametric surfaces


13


Fall Break

No class


14

16.7

Surface integrals of scalar functions



16.7

Surface integrals of vector fields

16.7 Surface integrals

Motivating examples

15

16.9

The divergence theorem

Quiz 9
Quiz 9 Key


16.8

Stokes' theorem

16.9 The divergence theorem and Stokes' theorem


16


Final Exam
6  8pm
on Wednesday 12/13/17
in Monteith 111
Cumulative

Review questions
Cheat sheet

