Mathematical modelling in Physics: deterministic processes

TL;DR

This paper reviews mathematical modeling principles in physics, emphasizing dynamical systems theory and its applications to scientific and engineering problems, highlighting the interdisciplinary connections and practical utility.

Contribution

It provides a comprehensive overview of mathematical modeling in physics, focusing on dynamical systems and their role in scientific and engineering applications.

Findings

Dynamical systems theory effectively models evolutionary processes.

Mathematical models from physics are applicable to engineering problems.

The relationship between modeling and other scientific disciplines is clarified.

Abstract

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics and applied for scientific and engineering problems. More specifically, the accent is placed on the theory of dynamical systems being used to produce evolutionary models. Classes of different models are presented and the relationship of mathematical modeling to other disciplines is outlined. The aim of the paper is to bridge together mathematical methods and basic ideas proved to be useful in science and engineering.