Math 2110 Learning Activities (Fall 2017)

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

A Few Useful Links:

3D Function Grapher (also does Parametric Surfaces!)

Learning Activities, By Week:

Week	Section	Topic	Learning Activities
1	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)
2	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)
	14.3	Partial Derivatives	Cross Sections
3	14.2	Limits and Continuity (*interesting topic, neither covered in class nor on exams)
	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
4	14.7	Maximum and Minimum Values	Max and Min Video Types of Extrema
	14.8	Lagrange Multipliers (*useful application, neither covered in class nor on exams)	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
5	15.2	Double Integrals over General Regions	Double Integrals over General Regions Video
	15.3	Double Integrals in Polar Coordinates
6		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
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) Summary of Triple Integrals (All Coordinate Systems)
8	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
9	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)
10	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)
11		Exam 2	Practice Exam 2 (solutions) Exam 2 Review Exercises
	16.5	Curl and Divergence
12	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)
13	16.7	Surface Integrals (Vector Fields)
	16.9	Divergence Theorem
14	16.8	Stokes’ Theorem	Summary of Surface Integrals (decision-making and methods)
		Final Exam Review