Labware - MA35 Multivariable Calculus - Single Variable Calculus
 MA35 Labs 1 » Single Variable Calculus Contents1.1 Functions of One Variable 1.1.1 Demo Tutorial 1.1.2 Linear Functions 1.1.4 Slices 1.1.6 Continuity 1.4 Integration Search

Demo Tutorial

Text

DEMO TUTORIAL

This tutorial is divided into five lessons.

To view a lesson, click on the [+] button above its picture and then click the button that appears.

A more detailed tutorial is located in the resources section.

Demos

 Lesson 1: Viewing a 2D Graph This 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 Window The 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 EXAMPLES at the bottom of this page for a list of some useful built-in functions.) To save the altered demo (don't worry, this won't overwrite the old one), select Show Applet Tag under Demo 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 Expressions In 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. The example used here 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 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. In this example, the variable c represents the altitude of the green line in the 2D Graph window.