1. Objectives
To become acquainted with the computer
lab and MATLAB by playing with and mimicking various commands, copying output
into a Word document, and printing to a local printer. First skim, and then carefully
read the entire assignment before
starting any tasks. The starred
questions are optional!
2. Starting MATLAB
Listen
carefully to the instructions given at the beginning of the lab session to find
out where MATLAB is on the public computers in B7 and how to start it. Remember everything, since you will need to
know it all when you start the homework on your own.
Running
MATLAB creates one or more windows on your monitor. Of these, the Command
window is the primary place where you interact with MATLAB. The character
string EDU» is
the MATLAB prompt in the Student Edition. Do not type it in the examples below.
3. MATLAB, the calculator
MATLAB can
do simple and advanced math just like a scientific calculator. Try typing
various mathematical expressions in the command window to see what
happens. The symbols for
multiplication, division, addition, and subtraction are *, /, +, and –. MATLAB can handle square roots, powers,
logarithms, and trigonometric operations using its own built-in functions. The
commands for sine, cosine, natural logarithm, and tangent are sin, cos, log, and tan respectively. To find the sine of 25 (in radians), for
instance, we would type
EDU» sin(25)
Task 1:
Use MATLAB to compute the expression sin(cos(ln25))+100(55/7-1000tan(.23))
ln is the symbol for natural log. Record the answer in a word document called LabOne.doc. Do this by highlighting the relevant lines in the MATLAB command
window with the mouse. Then click on 'Edit' on the menu bar and choose 'Copy.'
Now return to the word document and click on 'Edit' and choose 'Paste'. This
will paste the highlighted text from the Command window into your word
document. Label the pasted text in
boldface as Task 1.
4. Systems of equations*
As is only
proper for an application called MATrix
LABoratory, we can use MATLAB to
solve linear algebra problems. To solve
the system of equations
x + 2y + 3z = 366
4x
+ 5y + 6z = 804
7x
+ 8y + 0z = 351
we would type the following commands:
EDU» A = [1 2 3; 4 5 6; 7 8 0];
EDU» b = [366; 804; 351];
EDU» x = A\b
You should discover after typing the last line that the solution is x = 25, y = 22, z = 99.
Task 2:
Study the example to solve the system of
equations
x + y + z
= 16
x
+ y - z = -8
x
- y + z = 22
Copy the resulting answer in your word
document and label it Task 2.
5. Getting help in MATLAB
You should
become familiar with the help and lookfor commands; they will come in
handy later. If you type help followed by a function name
in the Command Window, MATLAB will display help for that function. For
instance, type
EDU» help sin
You can even
type help help. Unfortunately, to use help correctly you must know the
precise name of the function. The lookfor command differs from the help command by searching for
summary information instead of an exact match.
Task 3:
Compare the results of typing help
tangent and lookfor tangent in the Command window. Record the answers for each command in
your word document and label it Task 3.
6. Plotting**
Suppose you
want to plot y(x) =x2 for 0 ≤ x ≤ 4. This can be
accomplished in MATLAB with the following commands:
EDU» x= linspace(0, 4, 1000); %create a vector x with 1000 values from 0 to
4
EDU» y = x.^2; %create a vector y
whose values are the squares of the values in x
EDU» plot(x,y); %plot y vs. x
EDU» xlabel(‘x’);ylabel(‘y = x^2’)%label the x-axis of the figure ‘x’ and the
y-axis, ‘y = x^2’
Task 4:
Find out how to plot multiple graphs in the same
figure window using help plot. Use that
information, and a careful study of the commands above, to find the number of
points of intersection of the graphs of y1(x) =
cos(x) and y2(x) =
log(x)/log(3p) in the range 0.25 ≤ x ≤ 15. In MATLAB, pi
= 3.14159… Hint: what would PLOT(X,Y1,X,Y2) do? Record your answer in LabOne.doc and label it Task 4.
7. Just for fun
One day in a
pique of frustration, I typed in why at the command prompt and
was surprised to find that MATLAB accepted it.
See what happens.
8. Submitting Your Work
Type your
name (and your partner’s name if you have one), student ID, and the date at the
top of LabOne.doc. Print the document and sign it along with
your partner. Give the signed
assignment to the teaching assistant.
*The starred questions are
optional, but worth bonus points.