Math 2110 Learning Activities (Spring 2018)

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 Section:

Section Topic Learning Activities
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

Notes on Sketching and Identifying Surfaces

12.2 Vectors Visualizing Vectors in 3D

Vector Addition and Commutative Properties

Vector Components

Unit Vectors and Normalization

12.3 The Dot Product Dot Products in 3D

Direction Angles (*useful application)

Projections (*useful application)

12.4 The Cross Product Cross Products

Volume of a Parallelepiped (*useful application)

12.5 Equations of Lines & Planes Line in 3D (static) vs Line in 3D (variable)

Planes and Intercepts of Planes

An Example Relating Lines and Planes

14.1 Functions of Several Variables A Gallery of Examples

Level Curves of an (Elliptic) Paraboloid

Level Curves of a Gaussian Surface (Bell)

14.2 Limits and Continuity

(*interesting topic, neither covered in class nor on exams)

Limits Handout
14.3 Partial Derivatives Cross Sections
14.4 Tangent Planes and Linear Approximation Linear Approximation
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector Directional Derivatives Video

Directional Derivatives

14.7 Maximum and Minimum Values Max and Min Video

Types of Extrema

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


15.2 Double Integrals over General Regions Double Integrals over General Regions Video
15.3 Double Integrals in Polar Coordinates
Exam 1 Practice Exam 1 (solutions)

Exam 1 Review Exercises

15.6 Triple Integrals Modeling Solids Handout (Play-Doh!)

Surface Area Video (*helpful for Chapter 16)

Triple Integrals/Double Integrals in Polar Video

15.9 Change of Variables in Multiple Integrals

(*helpful and interesting, neither covered in class nor on exams)

Change of Variables Video
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)

Summary of Triple Integrals (All Coordinate Systems)

13.1 Vector Functions A Space Curve

Another Space Curve (Helix)

Line Segment

A Gallery of Examples



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

Practice Problems with Visualizations

16.2 Line Integrals (Scalar Functions)
16.1 Vector Fields Simple 2D Vector Field

Interesting 2D Vector Field

Simple 3D Vector Field

Interesting 3D Vector Field

16.2 Line Integrals (Vector Fields)
16.3 The Fundamental Theorem for Line Integrals Fundamental Theorem for Line Integrals Video
16.4 Green’s Theorem Green’s Theorem Video

Summary of Line Integrals (methods and deciding what to use)

Exam 2 Practice Exam 2 (solutions)

Exam 2 Review Exercises

16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas A Gallery of Examples

Practice Problems with Visualizations

Parametric Surfaces (from URI)

16.7 Surface Integrals (Scalar Functions)
16.7 Surface Integrals (Vector Fields)
16.9 Divergence Theorem
16.8 Stokes’ Theorem Summary of Surface Integrals (decision-making and methods)