Math 2110 Learning Activities (Spring 2018)

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

A Few Useful Links:

3D Function Grapher (also does Parametric Surfaces!)

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 Planes 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
13.2	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)