Calculus in Virtual Reality

Lessons about Calculus and Geometry in a VR setting

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:

3D Coordinates

- Rectangular 3D Coordinates

- Cylindrical Coordinate Measurements

- Cylindrical Coordinate Graphs and Regions

- Spherical Coordinate Measurements

- Spherical Coordinate Graphs and Regions

- Geometry of Vectors in 3D Quiz

Graphs in 3D

- Coordinates and Graphs in 3D

- Fundamental Planes

- Graphs in 3D

- Cylinder Surfaces

- Lines in 3D

- Planes in 3D

- Quiz on Lines in 3D

- Quiz on Planes in 3D

- Quadric Surface Playground and Exploration

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 Playground with user input (including dynamic vector and scalar calculations/visualizations)

- Plotting VVF

- Velocity

- Speed

- Arc Length

- Acceleration

- Unit Tangent Vector

- Unit Normal Vector

- Splitting of Acceleration

- Curvature

- The Binormal Vector

Vector Fields

- Vector Field Visualization Playground

- Plotting Vector Fields

- Divergence of a Vector Field

- Curl of a Vector Field

Multivariable Functions(Update coming in Fall 2021)

-Plotting Multivariable Functions

-Contour Plots

-Limits and Continuity

-Partial Derivatives

-Directional Derivatives

-Gradients

-Tangent Planes and Linearity

-Extrema of Multivariable Functions

-Extrema on Compact Regions

Vector Calculus

-Line Integrals of Scalar Functions

-Line Integrals of Vector Fields

-Surface Integrals (Coming Soon)

Integration (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.