Calculus in Virtual Reality (CalcVR)
Lessons about Calculus and Geometry in Virtual Reality!
We have added literal depth to calculus!
The CalcVR app uses a Google Cardboard headset to enable the user to visualize concepts in multi-variable calculus within a virtual reality setting. The user can specify their own objects for visualization as well go through lessons on the geometry and calculus of multi-variable functions and the corresponding surfaces. In addition to this, there are interactive demonstrations where the user can further explore the concepts covered in the lessons. Because these elements are rendered in a virtual the user can see the depth of these mathematical objects and the multiple facets at play in the study of these mathematics topics.
Users can use any Google Cardboard (v1.0, v2.0) or compliant viewer to work on lessons related to calculus and geometry in three dimensions. The headset should have a capacitive touch button or the user should use a Bluetooth controller
This app includes the following modules:
2D Coordinates and Graphs
- Rectangular 2D Coordinates
- Graphs and Sets
- Polar Coordinates (with two coordinate exploration demos)
- 2D Graph Demos (on conic sections, trigonometric functions, and lines in two dimensions)
3D Coordinates and Graphs
- Rectangular 3D Coordinates
- Lines and Planes (with two demos)
- Cylindrical Coordinates
- Spherical Coordinates
- 3D Coordinate Demos (with all three coordinate systems)
Curves and Surfaces
- Parametrizing Curves
- Parametrizing Surfaces
- Transformations of Surfaces
- Quadric Surfaces Demo
- Surface Plotting Demo (for parametric forms of surfaces)
Vector Valued Functions of 1 Variable
- Interactive Demo with user input (including dynamic vector and scalar calculations/visualizations)
- Intro to Vector Valued Functions
- Velocity and Speed
- Unit Tangent Vector
- Unit Normal Vector
- Splitting of Acceleration
- The Binormal Vector
- Vector Field Visualization Demo
- Plotting Vector Fields
- Divergence of a Vector Field
- Curl of a Vector Field
-Plotting Multivariable Functions
-Limits and Continuity
-Tangent Planes and Linearity
-Extrema of Multivariable Functions
-Extrema on Compact Regions
-Line Integrals of Scalar Functions
-Line Integrals of Vector Fields
-Surface Integrals (Coming Soon)
-The purpose of these materials is to introduce students to important ideas from multi-variable calculus in a virtual reality setting.
- These are not to be taken as a stand-alone set of materials, but instead are supposed to supplement student work and reading.
- We have designed these to work with either a single button interface or using a Bluetooth controller. We hope to add further functionality later, including sharks with laser beams on their head (not kidding about this, but sharks with lasers is harder than you think to implement...).
- It is very important to us that these materials are available and usable for the largest group possible. We have targeted the lowest required hardware restrictions possible. In the future we may develop more for the advanced VR sets, but Google Cardboard allows us to equitably engage the widest possible audience.
Changes to lessons on 3D coordinates, vector valued functions of 1 variable, lines, and planes to make the lessons more interactive and adapt to the feedback we have been given on their usage. Quizzes and Activities are now done in the CalcVR app as well as on our website, https://calcvr.org. We have removed the 2D lessons from the CalcVR app in favor of activities in the content section of our website, https://calcvr.org. We have also updated several visual elements to make sure that users can more easily read text and pick out visual elements.
Ratings and ReviewsSee All
Wow, this app has a lot of potential!!
However, music doesn’t work, the font is too small to read with ease, and it freezes when exiting the course.
Looking forward to see improvements :)
I’d love to share this with my students
With Family Sharing set up, up to six family members can use this app.