PHYCS 3730/6720 Lab Exercise

Exercise 1.

This is an introduction to Maple. Look at the New User Tour under the Help menu. There is a fair amount of material here, so for this lab, just glance over it, but read more carefully (1) (Working through the New User's Tour) and (3) (Numeric computations.) You can come back later to go through the other topics. (Nothing to hand in.)

Exercise 2.

Copy the Maple worksheet ~detar/public_html/lessons/maple_notes/maple_1.mws to one of your directories and work through it.
Do this by opening Maple with that file. Use the command xmaple maple_1.mws. (Nothing to hand in.)

Exercise 3.

Use Maple to help you find the solution to

    x = 6 e^-x.

to 4 significant digits. Do this in two ways:

Use fsolve. Note that to get e^-x in Maple you have to say exp(-x).
Use a fixed-point method. For this iteration you will have to invert the equation to put it in the form x = f(x) = -log(x/6). The Maple definition of the function is
```
    f := x -> -log(x/6)
```
Recall that the fixed-point method starts with an approximate value of the solution p₀ and then evaluates p₁ = f(p₀). The hope is that p₁ is a better approximation. This process is then repeated to convergence. In the file lab05 give the numeric answer and copy the Maple commands that you used to arrive at the answer in both cases.