Math 2110 Learning Activities (Fall 2016)

Need to Review Calculus 1 & 2 (1131/1132)?

Math Department Resources


A Few Useful Links:

Paul’s Online Math Notes, Calculus III

3D Function Grapher (also does Parametric Surfaces!)

2D Vector Field Generator

Learning Activities, By Week:

Week Section Topic Learning Activities Assessments
1 12.1 Three-Dimensional Coordinate Systems Visualizing the Octants

Points in 3D and Points in 3D (User Input)

Corners of a Box


Circles vs Cylinder/Line vs Plane

12.6 Cylinders and Quadric Surfaces Quadric Surfaces Understanding Surfaces Worksheet (Week 2)
12.2 Vectors Visualizing Vectors in 3D

Vector Addition and Commutative Properties

Vector Components

Unit Vectors and Normalization

Notes on Vectors (Week 1, not collected)
12.3 The Dot Product Dot Products in 3D

Direction Angles (*useful application)

Projections (*useful application)

Notes on the Dot and Cross Product (Week 1, not collected)
12.4 The Cross Product Cross Products

Volume of a Parallelepiped (*useful application)

Practice with Vectors Worksheet (Week 2)
2 12.5 Equations of Lines & Planes Line in 3D (static) vs Line in 3D (variable)

Planes and Intercepts of Planes

Lines and Planes Worksheet (Week 3)
14.1 Functions of Several Variables A Gallery of Examples

Level Curves of an (Elliptic) Paraboloid

Level Curves of a Gaussian Surface (Bell)

14.3 Partial Derivatives Cross Sections Partial Derivatives and Tangent Planes Worksheet (Week 5)
3 14.2 Limits and Continuity Limits Handout (Week 3)
14.4 Tangent Planes and Linear Approximation Linear Approximation
14.5 The Chain Rule Notes on the Chain Rule (Week 3, notes not collected but exercises will be)


Directional Derivatives and the Gradient Vector Directional Derivatives Video

Directional Derivatives

4 Exam 1 Practice Exam 1 and Solutions
14.7 Maximum and Minimum Values Max and Min Video

Types of Extrema

Notes on Absolute Maxima and Minima (Week 5, notes not collected but exercises will be)
5 14.8 Lagrange Multipliers Absolute Max/Min Video

Lagrange Multipliers Video

15.1 Double Integrals over Rectangles Double Integrals over Rectangles Video

Riemann Sum in 2D

Riemann Sum in 3D

Double Integrals and Volume Worksheet (Week 6)
15.2 Double Integrals over General Regions Double Integrals over General Regions Video
6 15.3 Double Integrals in Polar Coordinates
15.6 Triple Integrals Surface Area Video (*helpful for Chapter 16)

Triple Integrals/Double Integrals in Polar Video

Triple Integrals Worksheet (Week 7)
15.9 Change of Variables in Multiple Integrals Change of Variables Video Notes on Change of Variables (Week 6, notes not collected but exercises will be)
7 15.7 Triple Integrals in Cylindrical Coordinates Visualizing Cylindrical Coordinates

Triple Integrals in Cylindrical Video

15.8 Triple Integrals in Spherical Coordinates Visualizing Spherical Coordinates

Basic Shapes in Spherical Coordinates

Spherical Coordinates (from URI)

8 Exam 2 Practice Exam 2 and Solutions

Exam 2 Group Practice Problems

13.1 Vector Functions A Space Curve

Another Space Curve (Helix)

Line Segment

A Gallery of Examples

Vector Functions and Parameterized Curves (Week 9)
Application of Vector Functions (Week 9)
9 13.2


Derivatives and Integrals of Vector Functions
13.3 Arc Length Linear Approximation of Arc Length

Practice Problems with Visualizations

16.1 Vector Fields Simple 2D Vector Field

Interesting 2D Vector Field

Simple 3D Vector Field

Interesting 3D Vector Field

Vector Fields (Week 10)
16.2 Line Integrals Line Integrals (Week 10)
10 16.2 Line Integrals (continued)
16.3 The Fundamental Theorem for Line Integrals Fundamental Theorem for Line Integrals Video Line Integral Theorem Practice (Week 11)
11  16.4 Green’s Theorem Green’s Theorem Video
16.5 Curl and Divergence
12 Exam 3 Practice Exam 3 and Solutions
16.6 Parametric Surfaces and Their Areas A Gallery of Examples

Practice Problems with Visualizations

Parametric Surfaces (from URI)

Common Parametric Surfaces (Week 13)
13 16.7 Surface Integrals Line Integrals vs. Surface Integrals (Week 13)
16.9 Divergence Theorem Using the Divergence Theorem (Week 14)
14 16.8 Stokes’ Theorem
Final Exam Review Review for Final Exam and Solutions