Mathematica Activity: Visualising the Gradient

Static Fields 2021
Students use prepared Sage code to predict the gradient from contour graphs of 2D scalar fields.
What students learn
  • Model the gradient using a computer algebra system.
  • Visualize the geometric relationship between the gradient and the contours plot of a scalar field
  • Clarify how gradients look in two and three dimensions.

Use the Sage code at Using Technology to Visualize the Gradient to plot scalar functions of two variables, predict what a plot of the gradient looks like, and then check it.

Instructor's Guide

Student Task

This activity is a great follow up to Acting Out the Gradient. The students should know that the gradient is perpendicular to level curves (surfaces) and that its magnitude is the maximum slope. They use this information to predict the gradient vector field from looking at level curves for scalar fields. Then check their predictions with the Mathematica worksheet. The worksheet is open-ended and students can plot some scalar fields of their own.

Author Information
Corinne Manogue, Tevian Dray
Learning Outcomes