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PHYCS 3730/6720 Lab Exercise

Reading and references:
Note: If you are already familiar with Matlab, you may use it to do
this exercise instead of Maple. In that case you may skip the Maple
reading and Exercises 1 and 2 below. Please be sure to show the
Matlab commands you use to complete Exercise 3 below.

####
Exercise 1.

This is an introduction to Maple. Read through
the
Maple introduction . Start a Maple session and play with some of
the examples in these notes. (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 **p**_{0} and then evaluates
**p**_{1} = f(p_{0}). The hope is that
**p**_{1} is a better approximation. This process is then
repeated to convergence. In the file **Mylab05.txt** give the numeric answer and copy the
Maple commands that you used to arrive at the answer in both cases.
Note that you should use **evalf** to get digits instead of an
exact algebraic expression. (Another trick that does the same thing is
to insert a decimal point in the definition of **f** as
in **x/6.**.)