- animals
  1. zebra
  2. yak
- minerals
  1. calcium
  2. sodium

| Col1         | Col2     | Col3          |
| :----------- | :------: | ------------: |
| Left-aligned | Centered | Right-aligned |
| blah         | blah     | blah          |

```
  int x=1
  for (int i=1;i<=10;i++)
    x += i;
  printf("%d\n",x)
```

> this section will be set apart
> from the surrounding material

Octave

What is Octave?

Matlab is proprietary software, and can be quite expensive for some of the more state-of-the-art special toolboxes. Octave is a free and open-source clone of Matlab. It has essentially the same syntax and functionality, but is open-source and free!

Reference Links

• Octave-Forge provides further functionality and compatibility
• Categorical list of Octave/Forge functions.
• Octave manual
• Octave Mailing List
• Octave C++ API
• Web-based Octave
• Matlab Central
• Matlab Documentation
• Matlab Primer (worthwhile to print this out)
• Matlab Tutorial
• Matlab Info / Links
• Scilab is another good numerical environment.

Installing Octave

1. Download the installer and save it to your Desktop.
2. Double-click on the file you just downloaded to begin the installer.
3. Agree to the license and all default settings.
4. Your install is now complete, and you should have a shortcut to Octave on your desktop and in your start menu. You can delete the original installer.

Matlab/Octave Quick Introduction

• The up/down arrows conveniently allow you to scroll between previous commands.
• Put a semicolon at the end of a command to suppress output.
• Variables are case-sensitive.
• The example commands/output below should be self-explanatory.

>> A=[1 5 0 1000; 0 -3 1 200; 1 0 -1 0]
A =
         1         5         0      1000
         0        -3         1       200
         1         0        -1         0

>> size(A)
ans =
        3        4

>> A(1,4)
ans = 1000

>> A(2,:)
ans =
         0        -3         1       200

>> A(:,2)
ans =
         5
        -3
         0

>> B=A(1:3,1:3)
B =
         1         5         0
         0        -3         1
         1         0        -1

>> B'
ans =
         1         0         1
         5        -3         0
         0         1        -1


>> A([2,3],:)=A([3,2],:)
A =
         1         5         0      1000
         1         0        -1         0
         0        -3         1       200

>> rref(A)
ans =
        1        0        0      500
        0        1        0      100
        0        0        1      500
>> A\b
ans = 
      500
      100
      500

>> inv(A)*b
ans = 
      500
      100
      500

S=0; for k=1:100,   S = S + 1/k;   end; S

B=[0];
for k=1:40
  B(end+1) = 1.05*B(end) + 5500; 
end
printf("%2d %12.2f\n",[0:40;B]);
plot(0:40,B,'+')

load(eigen);
load(vect);
r(t):=[sin(t), cos(t), t];
define(v(t), diff(r(t),t) );
define(speed(t), sqrt(v(t).v(t)) );
define(T(t), unitvector(v(t)) );
define(a(t), diff(v(t),t) );
define(Tprime(t), diff(T(t),t) );
define(N(t), unitvector(Tprime(t)) );
define(aT(t), diff(speed(t),t));
define(aN(t), sqrt(a(t).a(t) - aT(t)^2) );
define(kurv(t), aN(t) / (v(t).v(t)) );
define(R(t), 1/kurv(t) );
define(B(t), express(T(t)~N(t)) );
float(v(1));
float(a(1));
float(aT(1)*T(1) + aN(1)*N(1));

f(x,y):=x^2+2*y^2;
g(x,y):=y-x^2+4;
solns:solve( [ diff(f(x,y),x)-L*diff(g(x,y),x), diff(f(x,y),y)-L*diff(g(x,y),y), 
               g(x,y)], [x,y,L])$
for soln in solns do (
  print(soln," f=",float(ev(f(x,y),soln))) );

load(draw)$
load(mnewton)$
f(x,y):=sqrt((x+1)^2+y^2)+sqrt((x-1)^2+y^2);
g(x,y):=(x^2+3*y-6)*(y-2)-3*x;
x0:-2; x1:2; y0:-2; y1:4;
draw2d(  grid = true, color = black,
    point_size = 5,point_type = filled_square, points([ [-1,0], [1,0] ]),
    color = blue,line_width = 4, implicit(g(x,y) = 0,x,x0,x1,y,y0,y1),
    line_width=2,
    color = red,         implicit(f(x,y)=2.03,x,x0,x1,y,y0,y1),
    color = orange,      implicit(f(x,y)=2.1,x,x0,x1,y,y0,y1),
    color = purple,      implicit(f(x,y)=2.5,x,x0,x1,y,y0,y1),
    color = forest_green,implicit(f(x,y)=3,x,x0,x1,y,y0,y1),
    color = brown,       implicit(f(x,y)=3.5,x,x0,x1,y,y0,y1),
    color = pink,        implicit(f(x,y)=4,x,x0,x1,y,y0,y1) 
)$
soln:mnewton([ g(x,y), diff(f(x,y),x)-L*diff(g(x,y),x), diff(f(x,y),y)-L*diff(g(x,y),y) ], [x,y,L], [1,.5,0]);
ev(f(x,y),soln);