LiveMath Tutorial for Chem 81

If you have correctly configured your browser for the LiveMath plug-in, you should see several graphs below. If you do not, click here for help. Work through this tutorial to get a flavor of the type of operations possible with LiveMath.

Simple Graphs: Move the mouse over the graph below and note that the cursor turns into a hand. You can grab it and move it around to see more of the graph. If you click and hold the mouse button down, a LiveMath context menu will pop up under your cursor. The only two entries that you're likely to use are the first, "Clarify," which can clean up a LiveMath display a bit, and "Display Precision," which we'll use later in this tutorial.

3-D Graphs: If you grab a 3-D graph (this one's an atomic wavefunction you might recognize from earlier courses!), you can rotate it in space to see all sides of the image. Holding down the "option" (Mac) or "Alt" (Windows) key as you drag changes the angles through which rotations occur. Try both ways here to see the effect. Dragging without the option key down will probably frustrate you!

Graph your own function: The graph below shows the trivial function y = x. You can edit this function, however, to plot just about anything. In the commands below, you can replace x by any number or expression.

To change a number

select it and type in a new number. You can double click to select the whole number.

To add the variable x

select what you want to add it to and type + x

To negate an expression

select what you want to negate and type -

To subtract the variable x

select what you want to subtract it from and type + - x

To multiply by the variable x

select what you want to multiply it by and type * x

To divide something by the variable x

select what you want to divide and type / x

To raise x to a power

select x and type ^ (shift-6) and the exponent, which can be any number, positive or negative, or an algebraic expression

To delete an expression

select what you want to delete and press your delete or backspace key. If you get a question mark, press the delete key again.

To type a function like sin(x)

type sin(x) (or cos, tan, sec, csc, arcsin, arccos, arctan, log (base 10 log), ln, cosh, sinh, tanh, or sech)

To type constants like pi or e

type e for e, 'p for pi, 'N for infinity, or i for i (the imaginary unit, the square root of -1)

If things become hard to read, click the Reload or Restore button to return everything to its original form.

Note the icons around the graph and in front of the equation. I'll turn these on whenever you need them.

The knife icon lets you drag a rectangle within a graph to expand the scale to the size of the rectangle. You can use it to see more detail in a particular region of a graph.

The rocket ship zooms you out by a factor of two in both graph directions. Hold down the "option" or "Alt" key when you click to zoom in.

The grid icons increase or decrease the number of points calculated and conected in the graph. Think of them as resolution buttons, but remember that increasing resolution, especialy in 3-D graphs, eats memory quickly.

Numerical calculations: While LiveMath is primarily a symbolic math program, it can also evaluate expressions numerically. In the example below, you can change xmin and xmax, the upper and lower limits to the integral. (The integrand is graphed and the range of integration is shown as a green line on the graph.) LiveMath will immediately update the numerical integration result. Click and hold down the mouse (Mac) or right-click (Windows) anywhere on the equations to bring up the LiveMath contextual menu. Select different Display Precision values (this sub-menu may not appear correctly with Microsoft Internet Explorer) and note the effect. The integral from 0 to 1 is exactly 1, but you'll see the precision of the numerical integration routine LiveMath uses if you set a 15 digit display precision!

Animations: LiveMath can also generate animations of graphs. The graph below shows two hyperboloid sheets that "kiss" at the origin when the parameter a = 0. The animation steps a through a range of values (which you can change - edit the choices below the graph), and if a = 0 is one of the values in the range, you'll see the sheets kiss. Note that the animation shows the frame number in the upper left and the current value for a in the upper right.