The Computing Engine
Matlab is a
calculator on Steroids
Has hundreds of builtin mathematical
functions that are built upon efficient
algorithms
Some simple examples:
Numerically computes most calculus concepts
such as derivatives and integrals
Matrix operations such as numerically solving
complex systems of equations

Quick Intro to Variables
Variables
Like on your TI83, you can assign variables to
remember answers, objects, and user input.
Example in Matlab:
x = 3;
Note: the semicolon suppresses the output on the command
line, try x = 3 without it and you will see!
Now you can use this variable x later in different
mathematical operations (if used in the command line
window, it is a global variable meaning it can be used
anywhere in Matlab)
Keep track of your variable names!!!!! 
Let’s add some numbers…
2 + 2 on the
command line
See the
answer that comes out
(hopefully 4)
The ans
variable
Stands for “answer”
Default variable for all common unassigned
operations done in command line window
See how it appears in the variable
workspace window? 
Order of Operations
PEMDAS
“Please Excuse My Dear Aunt Sally”
Parentheses, Exponent, Multiplication
Division, Addition, Subtraction
Try it out:
2 + 2 / 4 = 2.5
(2 + 2) / 4 = 1

Matlab and Matrices
The name Matlab
“Matrix Laboratory”
Originally an open application that came out
of the Argonne government research
institution (free!)
Initially designed for doing complex
algorithms involving matrices in linear
algebra and engineering applications 
Matrices in Matlab
A foundational
programming type
Representing it in Matlab:
A = [1 2 3; 2 0 2; 3 1 9]
Semicolons mean new lines, spaces between numbers
represent row placement (you can also use commas) 
More Matrices
Keep in mind that
a matrix can be a
single row! Some call this a vector.
A 3
element rowvector ( a 1x3 matrix) is
easy to type out, but what if you need a
100 element rowvector?
Try the
syntax:
t = 1:100 or
t = 1: 1: 100
What if you did “t = 1 : 0.01 : 100” ? 
Matrix Operations
Multiply a 3 x 3
Matrix with another:
A x B

Builtin Matlab Functions
Determinant of
our Matrix A
det(A)
Inverse of
our Matrix B
inv(B)

Builtin Matlab Functions
Some more basic
operations:
sqrt(4) – takes a square root of a number
mod(4,3) – modulus (we will use this later)
reciprocal(5) – gives the reciprocal of a number
cos(t) – gives the cosine of variable t
Note: if t is a rowvector, Matlab is adept enough to
recognize that it should take the cosine of each element
in t, and returns a row vector that is same length of t
exp(4) – represents e^{4}
log(4) – represents the natural log of 4 ( ln(4) ) 
Exercise!
Assign variables
x, y, a, b for different
values of a sine function
Put these
variables into a rowvector A
Plot A
over a domain of 4 values
Get a good
representative plot of a sine
function
Improve the “resolution” by
specifying more
values for the independent variable 
