JCalc |
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JCalc provides a convenient, easy-to-use user interface to the computer algebra system Maple. It is designed for students at the Calc III level or below.
Before you can use JCalc, you must have the "Java Runtime Environment 1.4" or better installed, and you must use a recent web browser such as at least IE 6, Mozilla 1.4, or Netscape 7. If you see a button labeled "Start JCalc" to the left you meet this requirement. Otherwise download that software and return to this page.
For further information on how to use JCalc, read the Tips and Tricks section below and work through the Examples below. Then start the program and consult the online help for further details.
JCalc Tips and Tricks
Here are some quick tips for using JCalc. For step by step instructions, see the examples below. Be sure to experiment!
- You enter expressions into the spreadsheet by clicking once on a cell, similar to
MS Excel. Then type the expression to enter into the input field at the top, using
the toolbar functions if you like. When you press ENTER the expression is evaluated,
properly rendered, and entered into the spreadsheet.
- Tip: To copy an existing cell into the cell you are currently editing, hold down the CTRL key while clicking on the cell to copy
- Tip: To re-evaluate an existing cell (perhaps you have applied some assumptions), hold down the SHIFT key while pressing ENTER
- To apply a procedure such as factoring or differentiation, first select the cell to which the operation should apply, then click on the appropriate button on the left. The operation will be applied to the selected cell and inserted below that cell.
- To plot a 2D or 3D function, first enter the function into an existing cell. Then
switch to the "Plot" tab on the left and click on "Add" to add your function to the
plot. You can add multiple functions to the plot by repeatadly clicking "Add".
- Tip: Not all combinations of options are available or applicable when plotting particular functions. If you get a "no plot available" message, adjust the options and click on "Draw" to redraw the function(s).
- Tip: You can plot multiple 3D surfaces easily. Enter the surfaces to plot into the spreadsheet, check the "3D" option on the Plot tab, then "Add" the surfaces to your plot. You can rotate, zoom, and pan using the 'keypad' buttons.
- You can enter HTML-formatted text into the "Expression" cells. Any text that starts with a double quote " will be formatted as HTML text, using the HTML tags you enter.
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Example 1: A Function and Its Derivative
In this example we will define a function, compute its derivative, and plot both the function and its derivative in one coordinate system. We will also see how to add descripive text to a JCalc sheet. Let's start with a new JCalc sheet.
- Click once on the top left cell. Click on the input field if necessary and enter
"<h1>My First Example</h1>"
Make sure to also enter the quotation marks. Then hit ENTER. The size of this cell will automatically adjust to accomodate your "headline" - Wile the second cell is highlighted, enter the expression
x^2*(1-x) / (x^2 - 1)
and press ENTER. The expression will show up quickly in the JCalc sheet and you can view a nicely formatted representation in the Math viewing area when you highlight this cell. - Highlight the cell you just entered and click on Factor. JCalc will factor (and reduce the fraction) and insert the result below the currently selected cell. Again, you can see a nicely formatted representation in the Math viewing area.
- Highlight the new cell containing the factored expression and switch to the Calc tab on the left. Enter the differentiation variable x in the field labeled with respect to next to the Differentiate button, then click that Differentiate button. JCalc will differentiate the expression and enter the result below the original expression.
- You might want to simplify the derivative by switching back to the Basic tab, then click the Simplify button to see a simplified form of the derivative.
- Highlight the derivative and right-click on that cell. Choose Insert Row to insert an empty row at that position. Click on that inserted row and type (including the quotes): "Derivative", followed by ENTER.
- Now switch to the Plot tab on the left. Highlight the original expression and click on Add. Then highlight the differentiated expression and click on Add again. You will see the graph of the function together with its derivative.
- Both functions are not continuous, so check the Discont. checkbox in the Options group. Then click on Draw to redraw your function. You should now see the proper graphs.
Example 2: Solving Equations Manually
In this example we will solve an expression manually, step by step, to understand the process better. While JCalc can of course solve an expression with one click, it is often advisable to manually manipulate an expression to better understand what is going on.
- Enter the following expression in a new cell. Use the "sqrt" button on the
toolbar to simplify the entry of the square root function:
sqrt(1 + sqrt(1 + x)) = 2
- To solve this equation manually, we first want to square both sides. Click on the Basics tab on the left. At the bottom of that tap you find the Apply operation, where the equation is represented by the symbol EQ. Make sure the expression you want to manipulate is currently selected in the spreadsheet.
- To square both sides of the equation, make sure the input next to the Apply button says EQ^2 by entering the appropriate symbols, then press Apply (or hit ENTER). Both sides of the equation are squared, removing one of the square roots. Note that a nicely formatted version of the equation is visible in the "Math viewer".
- Next we want to subtract 1 from both sides of the equation to isolate the root. Type EQ + 1 in the Apply's input file, then click Apply (or hit ENTER) to accomplish that.
- Now we have isolated the second root, so we can square the equation again. Type EQ^2 and click Apply.
- Finally we can subtract 1 from both sides of the equation to see the answer - do it.
To verify our answer, highlight the original expression sqrt(1 + sqrt(1 + x)) = 2 and click on the "Solve" button. JCalc will solve the equation immediately and insert the result below the selected cell.
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Example 3: Plotting a Maple Leaf
In this example we will plot an implicit equation in polar coordinates to learn more about the options available when generating 2D graphs.
- Enter the following equation r = r(t) in an empty JCalc cell:
r=(100/(100+(t-Pi/2)^8)) * (2-sin(7*t)-cos(30*t)/2)
As usual you can see a nicely formatted version of this equation in the Math viewer. - Now switch to the Plot tab and check off the Implicit, the Polar, and the Thick options.
- At this point the variables will have switched to r (radius) and t (angle),
which is perfect. Now enter the following ranges:
- r should go from -1.0 to 4.0
- t should go from Pi/2 to 3*Pi/2
- Finally you are ready to graph your masterpiece. Highlight the equation you entered in the JCalc sheet, then click the Add button of the Plot tab
You should see a curve in polar coordinates that resembles a Maple leaf.