** Matlab Help **

Matlab is availabile with limited online access from the
MyMath website;
after login, use "Goto" to follow the
"Software" link and select Matlab.
More information about Matlab is given at the
Matlab information website,
and the MyMath website.

Here is a Matlab example command for **plotting a simple function**
x^3-4x^2+4x-1, for x in [-1,3]:

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

Here are some Matlab example commands for **plotting two functions**
on the same graph:

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

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

Here are some Matlab example commands for finding a **best-fit line**
and plotting it with the data:

**
x = [5.8 1.5 2.3 1 3.3]; y = [8.6 1.9 3.1 1 5];**

p = polyfit( x, y, 1 ); m = p(1), b = p(2)

plot( x, y, '*', x, b + m*x )

title('Some Bird Eggs Data and Best-Fit Line')

xlabel('Egg Width'); ylabel('Egg Length')

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
**finding an approximate root** of f(x) = 1+sin(x)+x^3, for x in [-1,1]:

**
f = @(x) 1 + sin(x) + x^3; a = -1; b = 1; c = (a+b)/2; **

for i=1:8, if f(a)*f(c)<0, b=c;else,a=c;end, c=(a+b)/2; disp([a b c f(c)]); end

Some Matlab example commands for
**computing a sequence** a_{n+1}=1/(5-a_{n}),
with a_{1} = 1:

**
a = 1; disp([ 1 a ]), for i = 2:10, a = a/(5-a); disp([ i a ]), end **

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

**
f = @(x)x^log(x); a = 2; **

for i = 1:10, h = 1/2^i; disp([h (f(a+h)-f(a))/h]), end

Here is a Matlab command for
**plotting the implicitly defined function y(x)** defined by
x^2 + y^2 - 1 )^3 = x^2y^3 :

**
ezplot( '( x^2 + y^2 - 1 )^3 - x^2*y^3', [-1.5,1.5] )**

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:

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

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

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

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

x = a + Delta*[1:2:2*n-1]/2; M = Delta*sum(f(x));

disp(M)

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:

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

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

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

disp(T) % Trapezoidal Rule

O = f( a + [1:2:n-1]*Delta ); E = f( a + [2:2:n-2]*Delta );

S = Delta*( f(a) + 4*sum(O) + 2*sum(E) + f(b) )/3

disp(S) % Simpson's Rule

Here is a Matlab command for **plotting the surface** z = x^2+2y^2+4:

**
ezsurf('x^2+2*y^2+4')**

Note: Matlab does not orient the axes in the standard way, but
you can do this with the "view" command. For a more standard view, try

**
ezsurf('x^2+2*y^2+4'); view([135 15])**

Here are some Matlab commands for **plotting the surface** z = x^2+2y^2+4
and the **tangent plane** to the surface at (x,y,z)=(1,-1,7):

**
ezsurf('x^2+2*y^2+4'); hold on**

ezsurf('7+2*(x-1)-4*(y+1)');