** Computer Tools **

Matlab and Maple are available
with limited online access for WSU Math course students from the
MyMath website; after login,
just follow the "Software" link.
More information about Matlab can be found using the MyMath Matlab
help command. Math students at Washington State University may also use
Matlab in one of the Math Department
Labs .
Some sample Matlab commands are given below.

Here is a Matlab example command for plotting a simple function
x^3-4x^2+4x-1 :

**
ezplot( 'x^3 - 4*x^2 + 4*x - 1', [-1 3] )**

Some Matlab example commands for nested polynomial evaluation
of P(x) = 2x^4-x^3-4x^2+4x-1 at x0 = 3:

**
c = [-1 4 -4 -1 2]; d = 4; x0 = 3;**

P = c(d+1); for i = d:-1:1, P = c(i) + x0*P; end, disp(P)

Some Matlab example commands for
computing a table of values for the function
f(x) = (x^4+x-18)/(x^2-4) near x=2:

**
x = [1.9995 : .0002 : 2.0005]; **

f = (x.^4 + x - 18)./(x.^2 - 4);

disp([x' f'])

Some Matlab example commands for
computing an approximate derivative for x^ln(x) at x = 2:

**
h = 10.^(-[0:2:10]'); **

f = @(x)x.^log(x);

format long g

disp([2+h (f(2+h)-f(2))./h])

Some Matlab example commands for (approximately) finding a local
maximum of f(x)=x^3-4x^2+4x-1 and the point where the maximum occurs:

**
x = [-1:.01:2]; f = x.^3 - 4*x.^2 + 4*x - 1; **

[ M, j] = max(f); disp([M x(j)])

Some Matlab example commands for finding an approximation to the
definite integral of f(x) for x from 1 to 6 using the midpoint rule
with n = 32 points:

**
n = 32; a = 1; b = 6; h = (b-a)/n; **

f = @(x)x.^3 - 4*x.^2 + 4*x - 1;

disp( h*sum(f(a+h*[1:2:2*n-1]/2)) ) % Midpoint Rule

Some Matlab example commands for finding an approximation to the
definite integral of f(x) for x from 1 to 6 using the trapezoidal rule
and Simpson's rule with n = 32 points:

**
n = 32; a = 1; b = 6; h = (b-a)/n; **

f = @(x)x.^3 - 4*x.^2 + 4*x - 1;

T = h*( f(a) + 2*sum(f(a+h*[1:n-1])) + f(b) )/2;

disp(T) % Trapezoidal Rule

S = h*(f(a)+4*sum(f(a+h*[1:2:n-1]))+2*sum(f(a+h*[2:2:n-2]))+f(b))/3;

disp(S) % Simpson's Rule