Basic Functionality for One VariableThis section is divided into three lessons.Lesson 1: Viewing a 2D GraphThis demo includes two windows: a control window (which contains the equation for f(x, y) in this case) and a 2D Graph window. You may find it useful to adjust the size of the graph window. Once you are comfortable with the window size, you can translate or zoom in or out to change your view of the 2D graph. To translate, select Translate from the Tools menu or hold down Alt. Click and drag in the direction you want to translate the graph. To zoom, select Zoom from the Tools menu or hold down Shift. Click and drag upward to zoom in or drag downward to zoom out. When you are finished using the demo, you can exit by closing the control window or by selecting Exit Demo from the Demo menu in the control window.
Lesson 2: Using the Control WindowThe control window in this demo includes two elements: the interval x and the function f(x). Each time you change the information in a text box in the control window, you must press Enter for the change to take effect. For example, suppose you wanted to view the graph from x = –1 to 2 instead of –1 to 1. To do this, you would type in "2" in the text box for the upper bound of x and press Enter. In this demo, you have the option of changing the bounds on x, the resolution for x, and the expression for the function f(x). (See the table below for a list of some useful builtin functions.) To save the altered demo (don't worry, this won't overwrite the old one), select Show Applet Tag from the Demo menu in the control window. Copy the HTML code that appears, and paste it in your response to a homework assignment or discussion. This will create a button in your response that leads to your version of the demo.
Lesson 3: Variables and ExpressionsIn these demos, an expression can be assigned a constant or variable value and can then be used in any formula or plot in the demo. Here, the constant is called a, and it represents the magnitude of a vertical stretch of the graph. Try changing its value. You can change it to any number or to any expression involving c, the only variable used in this demo. Variables in the demos, like intervals, are given minimum and maximum values. Instead of having resolution, however, variables have "steps." If you start a variable at its minimum value, the amount of times you would have to press the ">" button to get to the maximum value would be equal to the number of steps for the variable. Just as the ">" button increases the variable value by one step, the "<" button decreases the value by one step. To see an animation in which the variable value keeps increasing or keeps decreasing until it reaches its upper or lower bound, use the ">>" or "<<" button, respectively. In this example, the variable c represents the altitude of the green line in the 2D Graph window.
Basic Functionality for Two VariablesThis section is divided into three lessons.Lesson 1: Viewing a 3D GraphThis demo includes two windows: a control window (which contains the equation for f(x, y) in this case) and a 3D Graph window. You may find it useful to adjust the size of the graph window. Once you are comfortable with the window size, you can rotate, translate, or zoom in or out to change your view of the 3D graph. To rotate, select Rotate from the Tools menu or hold down Control (hold down [Apple] if you are using a Mac). Now, click and drag the mouse in the direction you want the part of the graph closest to you to move. To translate, select Translate from the Tools menu or hold down Alt. Click and drag in the direction you want to translate the graph. To zoom, select Zoom from the Tools menu or hold down Shift. Click and
drag upward to zoom in or drag downward to zoom out. There are six other preset viewing angles under the View menu, each from some position on one of the axes. The shortcut keys for these views are x, y, z, Shift + x, Shift + y, and Shift + z. The shift button gives you a view from a point on the negativevalued part of the axis. Otherwise, the view will be from a positivevalued point. When you are finished using the demo, you can exit by closing the control window or by selecting Exit Demo from the Demo menu in the control window.
Lesson 2: Using the Control WindowThe control window in this demo includes three elements: the intervals x and y and the function f(x, y). Each time you change the information in a text box in the control
window, you must press Enter for the change to take effect. In this demo, you have the option of changing the bounds on x and y, the resolution for x and y, and the expression for the function f(x, y). (See the table below for a list of some useful builtin functions.) To save the altered demo (don't worry, this won't overwrite the old one), select Show Applet Tag from the Demo menu in the Ccontrol window. Copy the HTML code that appears, and paste it in your response to a homework assignment or discussion. This will create a button in your response that leads to your version of the demo.
Lesson 3: Variables and ExpressionsIn these demos, an expression can be assigned a constant or variable value and can then be used in any formula or plot in the demo. Here, the constant is called a, and it represents the magnitude of a vertical stretch of the graph (along the zaxis). Try changing its value. You can change it to any number or to any expression involving c, the only variable used in this demo. Variables in these demos, like intervals, are given minimum and maximum values. Instead of having resolution, however, variables have "steps." If you started a variable at its minimum value, the amount of times you would have to press the ">" button to get to the maximum value would be equal to the number of steps for the variable. Just as the ">" button increases the variable value by one step, the "<" button decreases the value by one step. To see an animation in which the variable value keeps increasing or keeps decreasing until it reaches its upper or lower bound, use the ">>" or "<<" button, respectively. In this example, the variable c represents the altitude of the green plane in the 3D Graph window.
Builtin Functions and Constants for Demo Software
Extending an Applet's FunctionalityThis tutorial is divided into two lessons.
Lesson 1: Adding Elements to a DemoThe ability to add and remove features of a given demo is a particularly nice feature of these demos. We show how to add features by starting with a ''blank'' demo, which has no predefined elements. Suppose that we wish to plot the graph of a function f(t) = t^{3} for t in the interval [0,3]. We would take the following steps:
Now that the demo has been created (modified), one can change the interval for t or the function f(t) in the control window.
Lesson 2: Using HotspotsThis demo shows a feature that is to available to all demos: the hotspot. In the Altitude of Line window, one can click on and drag the white (heavy) dot. The user can move this socalled hotspot up and down, and if it is connected to other pieces of the demo, then it will modify the other pieces according to its definition.
