===== Math 445 Mathematics and Applications in Matlab =====

Four goals
  - learn numerical programming 
  - learn applied mathematics 
  - explore applications 
  - think about science and society
  - grow in speaking, writing, reading, maturity


====Command line (REPL)====
  * Read an expression
  * Evaluate it
  * Print the result
  * Loop back --do it again!

example
<code matlab>
>> 4 + 5 
ans
  = 9
>>
</code>

====Arithmetic operators====

    +  plus  
    -  minus
    *  times
    /  divide
    \  divide
    ^  power
    %  comment

examples
<code matlab>    
>> 4^3
ans
  = 64

>> 4/3
ans
  = 1.33333

>> 4\3
ans
  = 0.75

>> 4+3  % write a comment here, Matlab will ignore it
ans
  = 12
</code>

====Precedence====
<code>
  ^      first
  * / \  next 
  + -    last
</code>

examples
<code>
>>  2*5^2-3/4+1
ans
  = 50.25

>> (2*5)^2-3/(4+1)
ans =
   99.4000
</code>

====Special numbers====
  pi   3.1415926...
  inf  infinity
  NaN  not a number
  i    imaginary unit
  j    imaginary unit for electrical eningeers!

<code matlab>
>> 1/0
ans =
   Inf
   
>> 0/0
ans =
   NaN
   
>> i^2
ans =
    -1
  
>> j^2
ans =
    -1
  
>> sin(pi)
ans =
  1.2246e-16  % wha...?
</code>

What does this mean? This is scientific notation shorthand: ''1.2246e-16''  means $1.2246 \times 10^{-16}$. So the answer is nearly zero. 

But why is ''sin(pi)'' not exactly zero? Because computers can store and compute only finite truncations of real numbers. Matlab can't represent $\pi$ exactly, only a truncation of $\pi$ that is accurate to sixteen decimal digits.
  
<code matlab>
>> 0.4 - 0.3 - 0.1
ans =
   2.7756e-17  % wha...?
</code>
Here the issue is that computers use binary representations of numbers, not decimal representations. None of the three numbers 0.4, 0.3, and 0.1 can be represented exactly in binary. They're instead represented with binary fractions very nearly equal to 0.4, 0.3, and 0.1. Usually you don't see the difference, but sometimes, like here, you do. 

====Variables====

<code matlab>
>> x = 4  % assign value of 4 to variable x
x = 
  4

>> y = 3 % assign value of 3 to variable x
y = 
  3

>> x*y   % evaluate x times y
ans =
  12

>> ans   % variable ans is value of last expression
ans =
  12
</code>
====Evaluating expressions====

If you want to evalue the same expression repeatedly with different variables, reset the value of the variables and use the arrow keys to "scroll up" to the expression. Then hit "enter"

<code matlab>
>> x = 3;
>> y = x^2 - 2*x + 5
y =
    8

>> x = 1; 
>> y = x^2 - 2*x + 5  
y =
    4
</code>
==== basic math functions ====

<code matlab>
  sin, cos, tan, sec, csc, cot, asin, acos, atan          % the classic trig funcs, in radians
  sind, cosd, tand, secd, cscd, cotd, asind, acosd, atand % the classic trig funcs, in degrees
  exp, log, log10, abs, sqrt, factorial, mod              % other awesome functions
</code>

  
  
====Workspace commands====

  help

  ; supress
  
  format compact
  format loose
  format long
  format short

  diary on
  diary off

  who
  whos 
  clear x
  clear all

  ls or dir
  pwd
  cd