“I'm no model lady.
A model's just an
imitation of the real
thing.”
Mae West
Mathematical Modeling
What is a model?
Models
• In physics we use math to
describe events
• A model is an equation that
describes a certain
phenomenon
Why use math?
Math
• Math is invariable
–Always gives the same
answer if the parameters
are constant
• Math is universal
–Very little subjectivity
Examples
• Meteorologist use models to
predict the path of a
hurricane
• For instance…
Hurricane Tracking
• There three types of models
–Statistical
–Dynamical
–Combination
• Each gives a probability of
path
Types of Models
• There are three types of
models we need to worry
about in physics
• Everything seems to come
in threes…odd
Linear Models
• You are already familiar with the
characteristic equation for this
model
Linear Model
• y is the dependant variable
• x is the independent variable
• m is the slope
• b is the y-intercept
What it looks like…
X Y
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
What is the equation?
Exponential Equation
• y is the dependent variable
• x is the independent variable
• a & b are just constants
• c is the y-intercept
What it looks like…
X Y
1 5
2 20
3 45
4 80
5 125
6 180
7 245
8 320
9 405
10 500
What is the equation?
Inverse
• y is the dependent variable
• x is the independent variable
• a is just a constant
What it looks like…
X Y
1 5.00
2 2.50
3 1.67
4 1.25
5 1.00
6 0.83
7 0.71
8 0.63
9 0.56
10 0.50
What is the equation?