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Visualizing_multivariable_functions_articles_

Having an image to hold in your head as you think about a multivariable function can be crucial for understanding that function. Graphs, contour maps, parametric functions, vector fields and transformations all providie different ways to visualize functions in higher dimensions.

Introduction_to_multivariable_calculus

Welcome to multivariable calculus! Soon you will learn how to apply to tools of calculus to multivariable functions, but to start things off let's start getting a feel for what these multivariable functions can actually look like.

Transformations

Thinking about a function as a transformation means thinking about how it moves points from the input space to the output space. A nice way to visualize this is with animations that actually move space.

Visualizing_vector_valued_functions

To understand vector-valued functions, it's common to either think parametrically, in which you think of the function as drawing a curve or surface in the output space, or with a vector field, in which you plop a vector on various points in space.

Visualizing_scalar_valued_functions

The main two tactics for understanding scalar-valued functions are graphs and contour maps.

Skill_check

Test your knowledge of the different ways to visualize multivariable functions.