Mathematical modeling techniques

Author: Xie Zhaohong
Publisher:
Publish Date: 2003-09-01
Features: This book is accompanied by a large number of exercises, aiming to help readers gradually master this technology through the combination of theoretical explanations and practical problem-solving. Through studying this book, readers can personally experience the omnipresence of mathematics and the immense potential of applied mathematics. It can serve as a textbook for university mathematics modeling courses in science and engineering disciplines, as well as a reference for scientists and engineers interested in or aspiring to work in mathematics modeling. To systematically and thoroughly analyze the object of study, grasp its characteristics and patterns, evaluate its static and dynamic performance, predict its trends, and make informed decisions for effective management and control, it is necessary to establish a mathematical model of the object. Mathematics modeling has become an indispensable foundation for systematic research and simulation of the characteristics of the object. Due to the increasingly important role of mathematics modeling technology in various fields of the national economy, its popularization and promotion have attracted the attention of governments worldwide. The United States began organizing national mathematics modeling competitions as early as the 1980s. Since 1994, China has also launched an annual national university mathematics modeling competition. Since mathematics modeling is a comprehensive technology based on disciplines such as mathematics, physics, biology, optoelectronics, mechanical engineering, economics, social sciences, and more, it requires that those engaged in or studying modeling technology not only have a solid mathematical foundation but also possess broad and comprehensive knowledge. To provide as much assistance as possible for the growing number of readers passionate about mathematics modeling technology, we have compiled this textbook. This book consists of nine chapters. The first three chapters introduce the concept of mathematics modeling, basic methods of model building, steps in model development, and how to conduct model validation. Starting from the fourth chapter, it elaborates on the corresponding mathematical modeling methods for different objects, categorized into discrete models, continuous models, differential and integral models, and probability and statistics models. The ninth chapter briefly introduces the usage of several commonly used mathematical software in the modeling process. The entire book begins with illustrative examples, guiding readers to develop modeling ideas and steps through the analysis and mathematical description of conventional phenomena, gradually deepening their ability to apply knowledge comprehensively.