Multivariable Calculus in VR

10.018 Modelling Space and Systems

Please choose the modules to guide your class activities with visualisation:

Partial Derivatives

Directional Derivatives

Multivariable Chain Rule

Critical Points

Global Optima (EVT)

Line Integral



   
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How to use the visualisation modules:

1) To change the graph, type in a new equation then press "Update graph"

Change equation

4) Rotate, zoom in/out of the graph using mouse or touchscreen

Rotate graph

2) Select the checkboxes in the GUI (controller) to see the visualisations

Update parameter

5) To view in Cardboard VR, close the controllers and press Cardboard logo

Cardboard mode

3) Some values with sliders can be typed manually with text input

Use sliders

6) You can also view in XR mode using Oculus Rift/Quest and HTC Vive

XR mode

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How to type in the equations:

You can generally use most types of equations, including:

  • Planes (e.g. 5*x+3*y-8)
  • Powers (e.g. (2*x^2)+y^3)
  • Square root (e.g. sqrt(x^2+y^2))
  • Trigonometric functions (e.g. sin(x^2+y^2), cos(x-(y/2)))
  • e (use capital E, e.g. cos(x)*(cos(y)*E))
  • π (use capital PI, e.g. PI*x^2+y)

    • To reduce ambiguity, use more explicit parentheses, e.g. use (2*x^2)+(y^3) instead of just 2*x^2+y^3