you ... can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
640:291:01
Part I: playing with arithmetic on Maple
9/15/2002
What I'd like you to type at the terminal will be in this typeface with numbers that look like this 1 4 7 9 and these suggestions will be indented about an inch. I'll ask you to hit the "enter" key (new line) with the request RET. Now, please, log in to eden and get a prompt in an x-window. Then type xmaple & RET The system should respond with a Maple screen on your display. There are standard ways for you to move or resize the screen, and various Maple-specific command possibilities. Maple is a huge program with a great many capabilities. We'll just explore a few of them. Right now I'd like you to move your mouse into the Maple window. You should see this, which is the command line: >| The symbol for your cursor is | and it is currently at an input line, indicated by the > sign. Please type 3+2 RET Maple did nothing with your input you only get another input line, and a complaint message from Maple! Move your cursor back (with the arrow keys or the mouse) to the first input line, and then move the cursor to the the end of the line. The input line should look like > 3 + 2| Then continue your typing with a semicolon followed by a return: ; RET Something should happen. You should get 5 and a new input line. You can move your cursor up and down. Now move your cursor back to your new input line. Type 17*3; RET and see what the result is. At the next input line type %+5; RET and explain the result. What do you think the meaning of the symbol % is? Now type the following to learn what ^ means. 2^3; RET But . . . I made a mistake! I wanted you to calculate the 300th power of 2. Please do the following: move your cursor back to the input line with 2^3 and position it in the following place: > 2^3|; and now type 00 and immediately hit RET. What happened? Please compute 3300 in the same fashion by moving your cursor and changing the input line. (Hint: position your cursor after the 2, type backspace, and then type 3.) What are the first 5 and last 5 decimal digits of this number? A little more: please type (look carefully here I'm asking for a colon, not a semicolon!) 5+6: RET You should immediately get another input line. Type (for example) %+7; and deduce what Maple does when an input line ends with a : (that is, a colon). Note that computations might and do occur which have results that are huge and silly to print out if you don't need them -- 2^(2^(2^(2^2))), for example. Try that sometime on your own, please, with ";" rather than a ":" and see what happens (hah!). Onward: please type 20; RET and see the result. Go back with your cursor and put a space between the 2 and the 0 and hit RET. What's the result? Now let's try 2*3+7; RET and observe that Maple follows the usual rules of precedence. Can you put parentheses in so that Maple will compute two times the sum of three plus seven instead? Remember to hit RET after you make the alterations. You should have gotten 20 as your answer, of course. If you did not make an error inserting the parentheses, go back and take one out (create an intentional error!) and then hit RET. What happens? haven't You broken anything. Let's keep exploring. Please get a new input line and try these commands in succession to learn how to do more arithmetic and to explore more features of Maple. OVER
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
2/3; RET Maple computes "exactly" and can do some (fourth grade?) arithmetic: %*300; RET Now try sqrt(2); RET and now %^2; RET so Maple knows the "meaning" of fractions and square roots or at least how to manipulate them. And now try (remember, if you mess up with a parenthesis or something else, just go back and do it again nothing is broken!): (sqrt(2)-1)^5; RET This result is puzzling. Sometimes Maple is lazy. Let's urge it to work by writing expand(%); RET That's better. But what if we want or need decimal approximations? Try evalf(sqrt(2)); RET Parentheses need to be matched always a source of anxiety as more and more complex expressions and commands are typed. What if we want more digits of 2? We can coax evalf to do this with more informed use. To see how, type help(evalf); RET Another screen should pop up. When I use Maple I tend to need a lot of help so the help screens accumulate on my display. You can "click" them on and off, and eliminate them entirely (click on the upper left or right corners of the screen to see how). Read the evalf screen until you can figure out how to get the first 100 digits (after the decimal point) of 2. I usually skip down to the examples on any help screen first, because they are usually relevant to my questions! What is the one-hundredth digit after the decimal point? Can you tell me the three-hundredth digit after the decimal point of 171/3 ? Use lots of parentheses, even in exponents, to inform Maple clearly what you want. Now try 1400/24; RET and we learn that Maple knows how to factor integers automatically. Can you get Maple to factor your social security number? How would you find a factoring command in Maple? If the first thing you try with the help command doesn't work, look at the references on the SEE ALSO line and check one of them. We can go on to try some algebra. But notice that you can stop your Maple session at any time in a variety of ways. One way that is polite to the system and also simple for you is to type quit RET and your Maple window will disappear, and you can exit the program by clicking on the File button. Of course all of your work will also have vanished, but at some other time you can explore various possibilities of saving what you've done.
Disclaimer! Non-advertisement!! Important information!!! Symbolic manipulation programs such as Maple are increasingly available. Mathematica and Derive are other programs with the same capability. There are many special purpose programs in science, engineering, and mathematics which have extensive "intelligence" to analyze models. We're considering Maple here because Rutgers has a site license for this program. It is generally available on Rutgers systems. The specific instructions won't be the same from program to program, but many of the same ideas will be present. Students should expect to have a machine do tiresome or elaborate symbolic computations as well as numerical computations.