Mathematical Modeling of Physical Systems: An Introduction PDF

PREFACE

This book is intended to provide the beginning student and the professional with an easily understood introduction to the topic of mathematical modeling. Modeling, which consists of assembling mathematical expressions as a description of a system or process, now permeates the daily lives of professionals, and an early introduction to the subject at the university level has become desirable, even mandatory.

The requirements for successful modeling are numerous, onerous, and complex. They comprise, first and foremost, an understanding of the underlying physics of the systems and the laws that govern them. Next in importance is the ability to make suitable simplifying assumptions, which will reduce the complexities of a system to manageable proportions while retaining a valid and realistic description of its behavior. In many instances this will mean that we shall have to content ourselves with upper and lower bounds to the solution.We term this "bracketing the solution," and it is surprising how often such bounds are all one needs to arrive at satisfactory answers. Choosing appropriate assumptions, however, is no easy task and requires a good "feel" for the system under consideration. It is as much an art as it is science, and it involves skills that can be acquired by only sustained practice. It is one of the aims of this text to provide that practice with numerous illustrations drawn from a wide range of disciplines. This policy of choosing examples from diverse fields is a deliberate one on our part. The route we have chosen is therefore a somewhat difficult one, but drawing on a wide range of concepts and physical laws ultimately proves more fruitful than a narrowly focused approach.