Visualizing scalar-valued functions
▶ Representing points in 3d
Learn how to represent and think about points and vectors in three-dimensional space.
▶ Introduction to 3d graphs
Three-dimensional graphs are a way to represent multi-variable functions with two inputs and one output. They're visualized by plotting input-output pairs in 3D space, resulting in a surface. Other methods of visualizing multi-variable functions include contour maps, parametric functions, and vector fields.
▶ Interpreting graphs with slices
3d graphs can be a lot to take in, but it helps to imagine slicing them with planes parallel to the x-axis or y-axis and relate them with two-dimensional graphs.
▶ Contour plots
An alternative method to representing multivariable functions with a two-dimensional input and a one-dimensional output, contour maps involve drawing purely in the input space.
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