Level Curves

Caution: Caution: TEMATH's tools will write the values of computed results at the bottom of this Report window. This will cause you to constantly scroll between the computed results and the instructions for this activity. You may want to print a copy of the contents of the Report window before you begin this activity.

Example 1: z = f(x, y) = sin(x) + sin(y)

The black curves represent positive values of z and the red curves represent negative values of z. As you move the cursor around the Graph window, note that the values of x, y, and z are given in the bottom three cells of the Domain & Range window. Additionally, an estimate of the min and max for the z values over the plot rectangle is written into the report window.

To add a level curve for a particular value of z,

You can change the default number of level curves drawn, the range of z values, and the thickness of the pen used for drawing the added level curves by selecting Level Curves... from the Options menu. Also, you can increase the grid size for more accurate plots but this will slow down the plotting speed.

To plot color and pattern density plots,

Example 2: z = f(x, y) = -3y/(x^2+y^2+1)

Example 3: Level Curves with an Artistic Flavor

Example 4: Equipotential Curves

The electric potential at a point (x, y) is given by V(x, y) = 1/sqrt(25 – x^2 - y^2). Plot some equipotential curves.

Example 5: Isothermals

The temperature of a metal plate at the point (x, y) is given by T(x, y) = 50/(1 + 3x^2 + y^2). Plot some isothermals.

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Copyright 2000-2008 Adam O. Hausknecht and Robert E. Kowalczyk