Math 2110 Learning Activities (Fall 2021)

A Few Useful Links:

GeoGebra Resources:

Graphing with GeoGebra: Intro to GeoGebra

Surfaces: Have a look at the equations and graphs of common surfaces

https://www.geogebra.org/3d/s52k8uur: Visualizing Traces and Partial Derivatives

Tangent Plane Demo: Visualize Tangent Planes and see their Connection to Partial Derivatives

Triple Integrals: See how to build up the domain of a triple integral and visualize if it is Type X, Y or Z.

Coordinate Systems: See how Cartesian, cylindrical and spherical coordinates work

https://www.geogebra.org/3d/unfhkaps:Line Integrals of Vector and Scalar Fields

https://www.geogebra.org/m/jb7z9wnb:Fundamental Theorem of Line Integrals

Collection of Demos: Student Selected Collection of Various Demos

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 Surfaces: Have a look at the equations and graphs of common surfaces in GeoGebra
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 https://www.geogebra.org/3d/s52k8uur: Visualizing Traces and Partial Derivatives in GeoGebra
14.4	Tangent Planes and Linear Approximation	Linear Approximation Tangent Plane Demo: Visualize Tangent Planes and see their Connection to Partial Derivatives in GeoGebra
14.5	The Chain Rule	Chain Rule Practice Exercises (with Solutions)
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 Lagrange Multipliers Practice Exercises (with Solutions)
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
15.6	Triple Integrals	Modeling Solids Handout (Play-Doh!) Surface Area Video (*helpful for Chapter 16) Triple Integrals/Double Integrals in Polar Video Triple Integrals: See how to build up the domain of a triple integral and visualize if it is Type X, Y or Z in GeoGebra
15.9	Change of Variables in Multiple Integrals	Change of Variables Video Change of Variables Practice Exercises (with Solutions)
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 on GeoGebra (use slider bars at top left to change variables) Summary of Triple Integrals (All Coordinate Systems) Coordinate Systems: See how Cartesian, cylindrical and spherical coordinates work using GeoGebra
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)	https://www.geogebra.org/3d/unfhkaps:Line Integrals of Vector and Scalar Fields in GeoGebra
16.3	The Fundamental Theorem for Line Integrals	Fundamental Theorem for Line Integrals Video https://www.geogebra.org/m/jb7z9wnb:Fundamental Theorem of Line Integrals in GeoGebra
16.4	Green’s Theorem	Green’s Theorem Video Summary of Line Integrals (methods and deciding what to use)
16.5	Curl and Divergence	The Idea Behind Curl Subtleties about Curl
16.6	Parametric Surfaces and Their Areas	A Gallery of Examples Parametric Surfaces (from URI)
16.7	Surface Integrals (Scalar Functions)	Practice Problems with Visualizations
16.7	Surface Integrals (Vector Fields)
16.9	Divergence Theorem
16.8	Stokes’ Theorem	Summary of Surface Integrals (decision-making and methods)