Maple Introduction Session Instructions

1. Start the Maple program.
First, start the program:  find the Maple 8 leaf icon and double click on it to start the program. You will have a clear, untitled worksheet to begin with. If you want to continue work on a file that has already been saved , you  can choose "Open" from the file menu (if you need help navigating the Windows or Mac file system, ask).

2. Do a few simple arithmetic problems.
Maple is quite a calculator -- you can type in expressions for Maple to compute (use +,-,*,/ for the four basic arithmetic operations, ^ for raising to powers). Be sure to end each statement with a semicolon. Some examples (you should make up your own):

>

3+88;

>

4^50;

>	37444*4532/100;

3. Assign some values to variables and use them.
Use :=  for assignments. Names of variables can be fairly exotic -- there are a few "reserved words" to avoid. Variables can stand for expressions, equations, lists of things, etc..

Also, Maple knows many standard functions:
sin(x), cos(x), tan(x), cot(x), sec(x), csc(x)  

The parentheses are REQUIRED in Maple, even though in standard math we sometimes omit them.
arcsin(x), arccos(x) , etc..
ln(x), log(x) -- both are the natural log -- log[10](x)  

exp(x)  -- for  -- note the parentheses, it is WRONG to say exp^x .
abs(x), sqrt(x)   --- also constants exp(1) , and Pi .

Use evalf  to get decimal values of Maple output.

Here are some examples -- you try these and some of your own:

>

z:=3+2*x;

>

a:=15;

>	sin(Pi*(z-a));

>

sin(a);

>	evalf(sin(a));

4. Maple commands:  solve, diff, int, subs, plot
These are how you get Maple to do real work -- solve  is for solving equations or systems of equations (there is also fsolve  for finding decimal appoximations of solutions of equations), diff for taking derivatives (ordinary and partial), int  for integrals, subs  for plugging values into expressions, and plot for drawing graphs.

All these commands have a basic    action(what,how);  syntax -- for example to use the plot command, you specify what to plot (i.e., which expression or expressions to graph) and how to plot it (i.e., what the domain is on the horizontal axis and range on the vertical one. You can also specify colors, styles, etc in the "how" part).  For example

>	plot({x^2,exp(-x)},x=-2..2,y=-1..3,color=blue,thickness=2);

Notice that the two things being plotted were enclosed  in braces { } -- this is required when you are plotting more than one graph.

The solve  command is syntactically the same -- solve(what,how)  -- "what" refers to the equation or equations being solved (again if there is more than one they must be enclosed in braces), and "how" refers to the name(s) of the variable(s) being solved for:

>	solve(x^2-5=0,x);

>	solve({3*x+2*y=5, x-y=0},{x,y});

Note -- solve just tells you what the answer is -- it does NOT assign any value to the variable.

Using the following examples, figure out the syntax of subs , diff  and int  (later you can read the sections of this Lab Manual on these commands to learn more):

>	subs(x=3,x^2+8);

>	diff(3*x^2+2*x+5,x);

>	int(6*x+2,x);

>	int(6*x+2,x=0..1);

Finally, fsolve  is used to solve equations numerically for decimal approximations of the answer -- you can specify an interval in which you wish to find a solution. For example:

>	fsolve(x^2-5=0,x,x=-3..-2);

This is useful when a plot reveals that there are solutions which solve  is unable to find algebraically.


5. Formatting, etc..
You have control over the fonts Maple uses for text -- when you are in Text mode (you can get to text mode by clicking on the "T" button at the top of the Maple window) you can choose a font from the pull-down menu. You can also use boldface  ,  italics , or underlined  characters by using Control-B, Control-I or Control-U, using the B, I    or U  buttons at the top of the window, or using the Format pull-down menu (it's a lot like a word processor).  More importantly, you can control the size  of everything in your worksheet -- there are three magnifying buttons at the top of the page -- small, medium and large. We use the large setting for demonstrations in class because it's easier to read, but you should use the small one for something you're going to print out.  Groups of statements will be bracketed in your worksheet unless you de-select "Show group ranges" in the "View" menu at the top of the window.

Text in your worksheet : It is important that you insert explanatory text into your homework papers -- to explain what your variables stand for, to interpret answers and to answer some of the essay-type questions we will ask, and to explain what went wrong if the answer doesn't come out right. To insert text at any point in your Maple Worksheet, position the cursor at the point you want to put the text, then click on the "T" button at the top of the window  - or just put the cursor at the beginning of a line and press Control-T. Maple will probably display your text in a different font, and will not attempt to execute your text as Maple statements. To get out of text mode and back into input mode, click on the [> button at the top of the page (you can also use Control-J to get a new input line after the cursor, or Control-K to get one before the current block of statements).

When you make plots in your worksheets, you can resize them or delete them by selecting them first -- just click the mouse anywhere in the plot to select the plot, use the little squares along the sides of the plot to resize it, or the delete key to delete it.

Finally, you can print and save from the File menu -- MAKE SURE YOU SAVE YOUR WORK OFTEN! In most computer labs, this will require you to have a floppy disk with you, or else you can use a file transfer program like FTP or Fetch to transfer saved files to a server.  -- Maple is a large complicated program and will occasionally crash -- you don't want to lose too much of your work by not backing up once in a while.

TASKS TO COMPLETE:

A. Define the two variables   y:=exp(-x)  and z:=sin(x)   -- don't forget the semi-colons.

B. Plot the graphs of y  and z  on the same axes --choose the horizontal domain so that at least two points of intersection of the two curves are visible (there are infinitely many and they all have positive x coordinates).  The statement you use to do the plot should be something like:

>	plot({y,z},x=-2..5);

C. Use fsolve  to find the x-coordinates of the two intersection points. You will have to specify the two intervals Maple should look in  (in two different statements). Take advantage of the definitions of y and z by using a statement of the form:

>	fsolve(y=z,x,x=0..3);

D.  Insert text into your worksheet telling why you picked the intervals you did.

E. Have Maple compute the derivative of x^x*cos(sqrt(1+x^5)) .

F. Print out your work (if the printer in your lab is working).

G. Save your file on the hard disk (choose "Save" or "Save As" from the File menu) -- it is ABSOLUTELY ESSENTIAL that the filename be of the form xxxxx.mws -- Maple will fill in the "mws" if you don't specify a file extension, but if you specify a different one, the file may behave strangely when it is reloaded. Then quit Maple (Exit under the File menu). Restart Maple, and load your file back in  -- and execute all its statements again (position the cursor on the first one, then keep pressing "enter").

H. Quit Maple again.

World-Wide Web

Undoubtedly, you have had a great deal of experience using a program like Netscape or Internet Explorer to explore the World Wide Web. We want you to know where you can find information on Penn's Calculus program, and all of the various resources available to you (electronic, personal tutoring, and computer support). Addresses on the Web are called "URLs", the general Penn URL is

http://www.upenn.edu

and the Math Department's URL is

http://www.math.upenn.edu

Information on the undergraduate mathematics program (including info on calculus courses and Maple) is at the URL

http://www.math.upenn.edu/ugrad/Undergrad.html


TASKS TO COMPLETE:

A. Get the Penn Math Department Undergraduate "Home Page" at the third URL given above.

B. Find the link (it will have a picture of a famous mathematician on it) to the "Home Page" of your course, and click on it to view this page.

C.  On your course home page, there will be links to the home pages of the professors and TAs teaching the course -- follow these links. Then go back to the course home page.

D.  Explore the pages that describe the various kinds of Math and Maple advising help that are available You can get to them by clicking on the "Help" link near the top of your course home page.

E. On the Home Page of your course, there are links to Maple demonstrations (examples). Go to the page that lists these examples. Click on one of them -- this will (should) cause your computer to "download" the Maple file for the demonstration from the Math Department computer. Your computer may ask you where to save the file (or what to do with the file). Be sure to remember where you saved it. Or (better), your computer may already be configured to open Maple and load the downloaded worksheet.

F. Quit your browser if Maple didn't open automatically. Then, open the file you just downloaded in Maple and execute its statements.

If time permits, you may wish to explore other parts of the Math Department Web or the Penn Web.