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MA35 Labs

1 Single Variable Calculus

2 Two Variable Calculus

3 » Three Variable Calculus

Polar Coordinate Labs

Two Variable Functions

Contents

3.1 Functions of Three Variables

3.1.1 Linear Functions

3.1.2 Domain, Range & Function Graphs

3.1.3 Slice Curves & Surfaces

3.1.4 Level Sets & Contour Surfaces

3.1.5 Continuity

3.1.6 Normal Vectors for Linear Function Graphs

3.2 Differentiation

3.3 More Derivatives

3.4 Integration

3.5 Vector Analysis

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Domain, Range & Function Graphs (Page: 1 | 2 )

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We can also construct a color graph of the function f by assigning to each point (x,y,z) in the domain a color that corresponds to the value f(x,y,z). In a color graph, each point has four coordinates. The first three are spatial coordinates and specify the position of the point in space, and the fourth coordinate indicates its color.

Demos

The 4D Color Graph

This demo shows the color graph of a function f(x,y,z) over the domain -1 {leq} x, y, z {leq} 1. Each point p = (x,y,z) in the domain is assigned a color according to the value of f(p). Blue indicates a function value of -2 or lower, green stands for -2/3, yellow indicates a value of 2/3, and red a value of 2 or higher. Use the hotspot on the top face of the cube to change the height of the top face. Moving the hotspot around, you can get a look at the the color distribution inside the cube.