# Mathematical Models for System

Mathematical models are used to develop systems.

## Relationship with data science

Many books titled "systems engineering" were published towards the end of the 20th century. Since the turn of the 21st century, the term " Data Science" has become a common word.

The mathematical model of the system that appears in "system engineering" is almost the same as the mathematical model that appears in data science. In data science, Machine Learning models are famous, and others are not often introduced. On the other hand, mathematical models of systems are mainly mathematical models that are useful when incorporated into systems, but there are also mathematical models that are useful when investigating and examining systems.

## Classification of Models

There are two classification, "Dynamic or Static", " Linear or Non-linear ", and " Direct problem and Inverse problem ".

Static is that the system do not depend on the time axis. Usually, dynamic model is written with ordinary differential equations. Differentiation is the model of time dependence.

### Studies of Dynamic System

Control Engineering is developed as a study of dynamic system. In control engineering, dynamic linear system is a main. Dynamic non-linear system is studied in Chaos .

### Studies of Static System

Regression Analysis is popular. "Functionality" of Quality Engineering means static linear system.