Mathematical Modeling: With Applications in Physics, Biology, Chemistry, and Engineering, Edition-2

Abstract

A mathematical model can be defined as an abstract model which uses mathematical language to describe the behavior and evolution of a system. Mathematical models are used widely in the many different sciences and engineering disciplines (such as physics, biology, chemistry and engineering). Mathematical models may have many different forms, including continuous time and discrete time dynamical systems (using differential equations an difference equations respectively), statistical models, partial differential equations, or game theoretic models. Mathematical modeling has an important role in the discovering the problems which occur in our daily life. Mathematical and computational models has been frequently used to help interpret experimental data. Models also can help to describe our beliefs about how different phenomenon around the world functions. In mathematical modeling, we try to transfer those beliefs and pictures into the language of mathematics. This transformation is very beneficial. First, Mathematics is an exact and delicate language. Second, we can easily formulate ideas and also determine the basic assumptions. The governed rules in Mathematics help us to manipulate the problem. Strongly speaking, in Mathematical modeling, we are using the results which have been already proved by mathematicians over hundreds of years. Computers play an important role to perform numerical simulations and calculations. Although, many of the systems in the real world are too complicated to model but we can solve this problem by identifying the most important parts of the system and then we include them in the model, the rest will be excluded. Afterward, computer simulations can be applied to handle the model equations and desired manipulations.