channelflow.org

Four goals

1. learn numerical programming
2. learn applied mathematics
3. explore applications
4. think about science and society
5. grow in speaking, writing, reading, maturity

• Read an expression
• Evaluate it
• Print the result
• Loop back –do it again!

example

>> 4 + 5 
ans
  = 9
>>

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

examples

>> 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

  ^      first
  * / \  next 
  + -    last

examples

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

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

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

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

What does this mean? This is scientific notation shorthand: 1.2246e-16 means . 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 exactly, only a truncation of that is accurate to sixteen decimal digits.

>> 0.4 - 0.3 - 0.1
ans =
   2.7756e-17  % wha...?

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.

>> 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

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”

>> x = 3;
>> y = x^2 - 2*x + 5
y =
    8
 
>> x = 1; 
>> y = x^2 - 2*x + 5  
y =
    4

  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

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