Mathematical modeling

Simulation - replacement of the object (the original) in its conventional way (model) and study the properties of the original by studying the properties of the model.

There are physical and mathematical models.

Mathematical model - a set of mathematical relations that reflect the main features of the object of the researcher.

The mathematical model is based on some simplification (idealization) and is an approximate description of reality.

An analysis of a mathematical model allows predicting the behavior of a real object.

The model is never the same as the real process.

The results obtained from the mathematical model only approximate the process.

A criterion for adequacy (matching) of a mathematical model and a real process is practice.

Mathematical models are widely used in physics, biology, and the like.

Example. The mathematical model of the body's trajectory with the initial velocity v at an angle a to the ground provided that the air is absent:

If from the first equation express:

and substitute in the second equation, we obtain:

For y = 0 we obtain the distance of the flight of the body:

This is the simplest model of the process of throwing the body in space.

Once a mathematical model has been created, it must be investigated, for example, in systems of computational mathematics.