Maple Lab 0 (Spring 2007 Math 251 Sections 05-07) 

Background Worksheet. 

Remember that even though this lab will not count towards your final grade, you must turn it in! 

It's a good idea to start every sheet with the restart command. Maple remembers everything that 

you do, so the restart command gives you a fresh start without having to shutdown and restart  

the program itself! 

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A Quick Note for Typing in Maple: 

To create new text groups such as this use the button labeled "T" above. To create a new execution group  

(the lines with maple commands which start with ">") you can use the button labeled "[>" or the keyboard  

shortcut "Ctrl+J". To insert a group before the cursor use "Ctrl+K".  

To delete a line of input or Maple output you can use the keyboard shortcut "Ctrl+Delete". To begin 

another line in an execution group use "Shift+Enter". Remember that "Enter" alone will just execute 

the command you've typed. 

Sometimes the commands we want to use are built into Maple. Other times we must load up a  

special package of commands to get the job done. To add commands we use the command  

"with(...);" 

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Warning, the name changecoords has been redefined 

To find out what all of these commands do we can ask Maple using "?". 

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This sphere is kind of rough. We can use the help to find a plot option to smooth it out.  

It looks like numpoints is a good way to go. 

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Let's play with vectors. We will include the vector calculus package and use rectangular (cartesian) coordinates. 

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Warning, the assigned names `<,>` and `<|>` now have a global binding 

Warning, these protected names have been redefined and unprotected: `*`, `+`, `-`, `.`, D, Vector, diff, int, limit, series 

Let's define two vectors. Call them "a" and "b". 

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We compute the "dot product" using a period between these two vectors. 

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You can compute the "cross product" of these two vectors using "&x". Let's call this cross product "c". 

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Now let's plot the vectors a and b and their cross product c along with the parallelogram spanned by the vectors a and b. 

Recall that the area of this parallelogram is equal to the length of cross product vector. 

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Let's create a vector length function. Recall that ":=" assigns the expression to the right to the name on the left. 

Also, "x -> y" means that "x" maps to "y". 

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You can see it is not hard to create your own functions.  

Actually in this case it is unnecessary. We can just use the "Norm" function to compute lengths. 

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Let's plot part of a line. First, let's define a vector function which describes our line and then use the plot command. 

Our line will pass through the point (1,2,3) and be parallel to the vector <4,5,6>. 

Notice that last time we defined a function it spit out a bunch of junk we really didn't want to see. So this time 

we'll end our function definition with a colon ":" instead of a semi-colon ";". This will suppress the output. 

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Notice all of the options I've added to the "spacecurve" command. What do they do? 

Now let plot the plane whose normal vector is <4,5,6> and which passes through the point (1,2,3). 

This plane's equation is "4(x-1)+5(y-2)+6(z-3)=0" 

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There are a number of different ways to do this. Let's check out a few. 

First, solve for z and use plot3d. The "solve" command will help us out. 

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Or we could use implicit plot and leave the equation in its original form. 

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Or we can "parametrize" the plane by letting x = s, y = t, and z = -4/6(s-1)-5/6(t-2)+3. 

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Let's say we want to plot several things together. For this, we use the "display3d" command. 

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