Math 2110 Learning Activities (Spring 2024)

A Few Useful Links:

Paul’s Online Math Notes, Calculus III

GeoGebra 3D Calculator

3D Function Graphing Tool (also does Parametric Surfaces!)

2D Vector Field Generator

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
14.7 Maximum and Minimum Values Types of Extrema
14.8 Lagrange Multipliers Lagrange Multipliers Practice Exercises (with Solutions)
15.1 Double Integrals over Rectangles Riemann Sum in 2D

Riemann Sum in 3D

15.2 Double Integrals over General Regions
15.3 Double Integrals in Polar Coordinates
15.6 Triple Integrals Modeling Solids Handout (Play-Doh!)

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 Practice Exercises (with Solutions)
15.7 Triple Integrals in Cylindrical Coordinates Visualizing Cylindrical Coordinates
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 https://www.geogebra.org/m/jb7z9wnb:Fundamental Theorem of Line Integrals in GeoGebra
16.4 Green’s Theorem 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)