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 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  
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 