The following is a brief introduction to some *Matlab* commands that
can be used to write the programs in Assignment 1.

To start *Matlab*, type `matlab` at the unix prompt.
When you see the prompt ">>", you can start entering
*Matlab* commands. To quit *Matlab*, select **Exit Matlab**
from the **File** menu.

Help on using *Matlab* commands by clicking on **Help**
and following the links.

Matlab programs should be stored in files, called `program` at the *Matlab* prompt ">" will execute all the
statements in the program. However, before doing so, be sure that
your current directory is the one containing the file **Current Directory** and change
to that directory.

To place comments in your program, use the % sign
before any line you wish as a comment. To avoid intermediate output
produced by *Matlab*, place a semicolon at the end of any statement
whose output you do NOT want *Matlab* to display on the screen.

format long -- arithmetic with 14 decimal places (the default is format short -- 4 decimal places). for loops: These have the form: for i=1:10 statements end if, else statements: These have the form if a <= b statement else statement end norm(u, inf) -- computes maximum of the absolute values of the components of the vector u. norm(u,1) -- computes the L_1 norm of the vector u, i.e, the sum of the absolute values of the components of u. norm(u, 'fro') -- computes the L_2 norm of the vector u, i.e the square root of the sum of the squares of the components of u. To enter a row vector intoMatlab, type v = [1 2 3] or v = [1,2,3] If you wish v to be a column vector, then enter v= [1 2 3]' or v = [1; 2; 3] If v = [1 2 3], then w = [v 4] gives the row vector [1 2 3 4] To solve the linear system A x = b, type x = A\b; Be careful about the direction of the slash symbol. The symbols <, <=, >, >= have the obvious meanings. * is multiplication, / is division. If v is a row vector, v*v' produces a scalar, v'*v produces a matrix and v.*v produces another row vector in which the multiplication is performed separately on each component. In general, placing a period before an algebraic operation means to perform the operation on each component of the vector. sqrt(2) produces the square root of 2; log(2) gives the natural log of 2 To see the list of other elementary functions, typehelp elfunTo plot a sequence of points stored in the vectors (x,y), typeplot(x,y). Note that for Assignment 1, the approximate solution will be stored in a column vector u of length n-1, where n is the number of subintervals. If you wish to plot the solution, this may be done as follows. upic = [0; u; 0] % this adds the values of u at the endpoints of the interval, which are not included in the solution vector The coordinates of the corresponing x values can be obtained by using a for loop, or more simply by the statement. xpic = 0:1/n:1 % this produces a vector [0, 1/n, 2/n, ... , 1] Then plot(xpic,upic) produces the plot.