Welcome
Syllabus
Schedule
Homework
Project

Multivariable Calculus
Math 2110Q § 003
Fall 2017

Schedule

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 multi-variable domains
Bivariate functions in Desmos

A robust 3D grapher
14.3
Partial derivatives
Higher-order 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 multi-variate 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 vector-valued 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
16.7 Surface integrals of scalar functions
13

Fall Break No class
14
16.7
Surface integrals of vector fields
16.9 The divergence theorem
15
16.8
Stokes' theorem
16

Final Exam

6 - 8pm on 12/13 in Monteith 111

Cumulative