This app uses a Google Cardboard viewer to allow the user to visualize the concepts of multi-variable calculus in 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. The rendering of these elements in a virtual environment is important since that allows the user to see the depth of these mathematical objects and helps the user to see 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.
This app includes the following modules:
Lesson1-1: Two Dimensional Rectangular Coordinates
Lesson1-2: Regions of Space in Two Dimensions
Lesson1-3: Polar Coordinates
Lesson 1 Gallery: Demonstrations on coordinates in two dimensions, conic sections, lines, and trigonometric functions.
Lesson2-1: Three Dimensional Rectangular Coordinates
Lesson2-2: Planes and Lines in Three Dimensions
Lesson2-3: Cylindrical Coordinates
Lesson2-4: Spherical Coordinates
Lesson 2 Gallery: Demonstrations on Coordinates in three dimensions, lines and planes, and quadric surfaces.
Lesson3-1: Parameterizing Curves in Space
Lesson3-2: Parameterizing Basic Surfaces
Lesson 3-3: Parameterizations and Transformations of Graphs
Lesson 4 (upcoming) will be about the calculus of vector valued functions of one variable.
-The purpose of these materials are 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 no button (just stare for a couple seconds for a click) or single button interface. We hope to add further functionality later, including Bluetooth controller support and 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 offer to equitably engage the widest possible audience.