Introduction

While the new Desmos-3d application is still in beta, it is eminently usable! You can plot explicit and implicit surfaces, space curves, vectors and vector fields, and your plots can be dynamic in multiple ways. The links below take you to Desmos demos that you are free to copy and modify to suit your needs.

Here are some of the features of Desmos that make it effective for classroom demonstrations:

• implicit, explicit and parametrically defined curves and surfaces.
• animation and control of parameters via sliders
• domain restriction (indeed essentially arbitrary restrictions of the portion of a graph to be drawn)
• list comprehensions
• procedures

Those last two make the system more-or-less as powerful as a full-blown CAS.

2d plots for use in Multivariable Calculus

Contour plots

• Contour plots for the monkey saddle.

Explicit/implicit/parametric representations

• Three ways to draw a circle.
• The involute of a circle.

Lagrange multipliers

• Visualizing contours of the objective function and the constraint.
• Finding the minimum distance between a point and a curve

Regions of integration

• Integrals over certain regions sometimes force a particular order of integration.

Vector fields

• A hack to draw vector fields in the plane.

3d graphs in Desmos

Quadric surfaces

• All of the surfaces defined by quadratic polynomials in 3 variables.
• Hyperboloids of 1- and 2-sheets and a cone -- and how they fit together.

Limit funny business

• Limits in higher dimensions can fail to exist for interesting reasons.

Directional derivatives

• Visualizing the directional derivative.

Tangent Planes

• Visualizing the tangent plane to a surface at a point.

Spacecurves

• Circular motion in 3 space with the Frenet frame visualized.
• Motion along a helix.
• Exploring a theorem about the derivative of a constant length vector.

Parametric surfaces

• Parametric surfaces including a sphere, a cone, and cylinders.

Multiple Integrals

• A simple double integral that admits an easy geometric check on the resulting volume.
• Worst case scenario for the region in a triple integral.

Vector fields

• A couple of 3d vector fields: gravity, a tornado (not really), and something with a source and a sink.