A mathematical model uses mathematical descriptions, functions, and equations to represent real-world situations in a simplified way. There are three main types of mathematical models: linear models which use linear functions, quadratic models which use quadratic functions, and exponential models which use exponential functions. The process of developing a mathematical model involves making assumptions and simplifications, representing the situation using functions or relations, then comparing predictions from the model to real data.

2. A mathematical model is the mathematical
description of a real situation.
In developing the model, some
assumptions are made and we consider
some simplifications of reality.
A model can represent it using:
• Relations
• functions

3. There are three types of models:
•Linear model: We call
linear models to situations
can be represented by a
linear function. can be
determined graphically or
by means of an equation.

4. • Quadratic model: We say
that the model is quadratic
if we can express by means
of a quadratic function.
A quadratic model can be
determined through an
equation or by means of a
graph that made the best
approximates of the data.

5. • Exponential model: We call
exponential models to
situations that are
represented by an
exponential function.
The exponential models are
very common in the study
of population increases, the
calculation of bank interest,
so as various physical
phenomena.

6. The process for develop a mathematical model is as
following:
4.Compare the data obtained as
predictions with real data. If the data
are different, the process is restarted.

7. A single differential equation mathematical
model can be of many different phenomena.
a mathematical model is formed by an initial
value problem, or also value problem at the
border.

8. • An analysis of the spread of a contagious flu, for
example, is reasonable to assume that the rate or
reason that spreads not only is proportional to the
number of people, x (t), which have contracted at time
t, but also the number of subjects, and (t), which have
not yet been exposed to infection. If the rate is dx / dt,
then
• Where k is the usual constant of proportionality.

9. • If, for example, introduces
an infected person in a
constant population of n
people, then x and y are
related by x + y = n + 1.
We use this equation to
eliminate and in equation
(1) and obtain the model
• An obvious initial condition
accompanying equation
(2) is x (0) = 1.