**A Few Useful Links:**

Paul’s Online Math Notes, Calculus III

3D Function Grapher (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 Video |

14.7 | Maximum and Minimum Values | Max and Min Video |

14.8 | Lagrange Multipliers | Absolute Max/Min Video |

15.1 | Double Integrals over Rectangles | Double Integrals over Rectangles Video |

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 |

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 | 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 |

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) |