I explain here how I use maple to respond to an e-mail query like the one below:
To: firstname.lastname@example.org From: email@example.com Subject: HELP!!!! For the last 72 hours I have been trying to solve the equation x y' + y = 1. I'm beginning to think that it doesn't have a solution. Please help me!!! Jimmy Goober P.S. My roomate wants me to ask you what the integral of x^2 sin(7x) is.
I shall now dispose of these questions in a few simple keystrokes. First, I start an e-mail message to Mr. Goober in an xterm using an editor like vi. Then I fire up maple in another xterm by typing
NOTE: That's maple, not xmaple. I want the ASCII terminal version of maple for this task.
After I type maple, I see
hua-231% maple |\^/| Maple V Release 4 (WMI Campus Wide License) ._|\| |/|_. Copyright (c) 1981-1996 by Waterloo Maple Inc. All rights \ MAPLE / reserved. Maple and Maple V are registered trademarks of <____ ____> Waterloo Maple Inc. | Type ? for help. >
Next I type the following commands at the > prompt.
> Diff(y,x) + (1/x)*y= 1/x; dy -- + y/x = 1/x dx > u(x)= exp( Int( 1/x , x ) ); / | u(x) = exp( | 1/x dx) | / > Int( x^2 * sin(7*x) , x) = int( x^2 * sin(7*x) , x ) + C; / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | /
To answer Mr. Goober in a prompt and courteous fashion, I shall click with my left mouse button at the start of a portion of maple output that I want to copy to my e-mail and then I shall click with the right mouse button at the end of the text to select it. Then I shall click with the middle mouse button while in input mode of vi in my e-mail to insert the selected text from maple in the e-mail. (If you're a dexterous mouser, you can left mouse click and drag over the text to select it ---and then right mouse click to adjust the ending point.)
Note: If you use vi, you'll want to set your wrapmargin to zero before you glob text into your file with the middle mouse button. To do this, simply type
in command mode of vi.
Here is the result of my efforts:
Dear Mr. Goober, Notice that you can divide your ODE by x to obtain dy -- + y/x = 1/x , dx a first order linear ODE in standard form. The integrating factor will be / | u(x) = exp( | 1/x dx ) = x . | / Use this as in Section 1.3 of B & D to get the solution in the back of the book. See you in class on Monday? P.S. Tell your roomate / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | /
As you can see, this is also a nice way to display mathematics on the web. That last equation was set in HTML via
<P> <PRE> / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | / </PRE>
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