物理数学

Mathematical Modeling of Physical Systems from Theory to Practice

Abstract

Aouam Penko*

Mathematical modelling stands as a cornerstone of scientific inquiry, bridging theoretical concepts and real-world phenomena. By translating physical systems into mathematical language, models provide a structured way to understand, predict, and manipulate the behaviors of these systems. This journey from theory to practice involves abstract formulation, computational implementation, and empirical validation, creating a comprehensive framework that advances knowledge and technology. At its core, mathematical modeling begins with the abstraction of a physical system. This involves identifying the essential features and relationships within the system, while disregarding extraneous details. For instance, in classical mechanics, the motion of a projectile can be simplified by ignoring air resistance and assuming a uniform gravitational field. This simplification leads to the formulation of differential equations that describe the system's dynamics. Such equations capture the fundamental laws governing the system, providing a mathematical representation of physical principles like Newton's laws of motion.