Calculus in Virtual Reality 2.30

Nicholas Long – Freeware – iOS
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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 utilize any Google Cardboard (v1.0, v2.0) or compliant viewer to engage with 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:
<ul>
 <li>3D Coordinates 
 <ul>
 <li>Rectangular 3D Coordinates</li>
 <li>Cylindrical Coordinate Measurements</li>
 <li>Cylindrical Coordinate Graphs and Regions</li>
 <li>Spherical Coordinate Measurements</li>
 <li>Spherical Coordinate Graphs and Regions</li>
 <li>Geometry of Vectors in 3D Quiz</li>
 </ul>
 </li>
 <li>Graphs in 3D
 <ul>
 <li>Coordinates and Graphs in 3D</li>
 <li>Fundamental Planes</li>
 <li>Graphs in 3D</li>
 <li>Cylinder Surfaces</li>
 <li>Lines in 3D</li>
 <li>Planes in 3D</li>
 <li>Quiz on Lines in 3D</li>
 <li>Quiz on Planes in 3D</li>
 <li>Quadric Surface Playground and Exploration</li>
 </ul>
 </li>
 <li>Curves and Surfaces
 <ul>
 <li>Parametrizing Curves</li>
 <li>Parametrizing Surfaces</li>
 <li>Transformations of Surfaces</li>
 <li>Quadric Surfaces Demo</li>
 <li>Surface Plotting Demo (for parametric forms of surfaces)</li>
 </ul>
 </li>
 <li>Vector Valued Functions of 1 Variable
 <ul>
 <li>Interactive Playground with user input (including dynamic vector and scalar calculations/visualizations)</li>
 <li>Plotting VVF</li>
 <li>Velocity</li>
 <li>Speed</li>
 <li>Arc Length</li>
 <li>Acceleration</li>
 <li>Unit Tangent Vector</li>
 <lIUnit Normal Vector/liI
 li"Splitting of Acceleration""choosen finale"/llo
eli!Bi normal etort Vector/liI
 ulI/liI
lIi Fields
i!Vector Field Visualization Playground 
Plotting Vector Fields
Divergence of a Vector Field
Curl of a Vector Field
 iriable Functions(Update coming in Fall 2021)
Plotting Multivariable Functions
Contour Plots
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