Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens.

The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented.

Features

• Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well
• Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding
• Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.

Table of Contents

1. Foundations of mathematical modeling

Part I. Systems with lumped parameters

2. Approximate solving of differential equations

3. Mechanical oscillations

4. Electrical oscillations

5. Elements of dynamical system theory

6. Mathematical models in chemistry

7. Mathematical model in biology

8. Mathematical model of economics

9. Mathematical models in social sciences

Part II. Systems with distributed parameters

10. Mathematical models of transfer processes. 1

11. Mathematical models of transfer processes. 2

12. Wave processes

13. Mathematical models of stationary systems

14. Mathematical models of fluid and gas mechanics

15. Mathematical models of quantum mechanical systems

Part III. Other mathematical models

16. Variational principles

17. Discrete models

18. Stochastic models

Part IV. Additions

19. Mathematical problems of mathematical models

20. Optimal control problems

21. Identification of mathematical models

About the Author

Simon Serovajsky is a professor of mathematics at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.