# MTH 243 Calculus III First Computing Project

Your assignment is to submit electronically a MATLAB m-file (also known as a script) that

accomplishes the tasks below. To submit your notebook, go to “Computing Projects and

Materials” at the BB site and click on “Second computing project”.

A demo m-file is provided for this project. It is called “MTH 243 first computing project” and is

found at the same BB area as this project itself. It is recommended that you complete this project

by launching this demo m-file, modifying it as needed, and saving the result as your own. The

output of the demo is two plots (in separate windows) of a) the graph, and b) the curvature  t 

for the given vector-valued function r t  . Actually the demo file performs this for two separate

curves, namely   2 3 r t  t, t , t , 0  t 1 and r t   2sint, t,3cost , 0  t  4 .

Your first step should be to launch the demo and execute

each example. (The %% symbol is the standard way to

divide an m-file into separate sections; whichever

section your cursor is in is the “active” section, and then

the “Run Section” command shown (or simply Ctrl-

Enter) executes the code in that section.)

Unfortunately MATLAB makes the two plots exactly

the same size and puts them in exactly the same place on your screen, so it looks as though you

only got one graph; in reality you have to use your mouse to slide the top graph away from the

bottom one. Having done so, use your mouse to rotate the graph of r t  in 3D, and stop to think

about the curvature graph; does the graph of r t  actually look more curved, or less curved,

where the graph of  t  claims that it is?

What your m-file needs to do is produce a graph of r t  , and of  t  , for each of the following

curves. In each case you will simply modify the code provided in the demo to produce the

graphs you want. You’ll need to revise not only the definitions of r t  and of its domain, but

also the viewing window for the graph of r t  . Use %% as in the demo to divide your m-file into

sections, with appropriate labeling.

1. r t   sint, t,cost , 0  t  4 . (This is a simplified version of one of the examples; is

the graph of  t  surprising?)

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