A Few Useful Links:
Paul’s Online Math Notes, Calculus III
3D Function Graphing Tool (also does Parametric Surfaces!)
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 |
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 |
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) |
14.1 | Functions of Several Variables | A Gallery of Examples |
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 |
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 |
13.2 | Derivatives and Integrals of Vector Functions | |
13.3 | Arc Length | Linear Approximation of Arc Length |
16.2 | Line Integrals (Scalar Functions) | |
16.1 | Vector Fields | Simple 2D 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 |
16.6 | Parametric Surfaces and Their Areas | A Gallery of Examples |
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) |