## 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

>> 4 + 5
ans
= 9
>>

### Arithmetic operators

+ 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

### Precedence

^ first
* / \ next
+ - last

examples

>> 2*5^2-3/4+1
ans
= 50.25
>> (2*5)^2-3/(4+1)
ans =
99.4000

### Special numbers

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.

### Variables

>> 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

### 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”

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

### basic math functions

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

### 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