Mathematical Modelling by J.N. Kapur: A Comprehensive Guide
Mathematical modelling is the process of using mathematical tools and concepts to describe and analyze real-world phenomena. It is a powerful and versatile technique that can be applied to various fields of science, engineering, economics, social sciences, and more.
One of the most influential books on mathematical modelling is Mathematical Modelling by J.N. Kapur, published in 1988. This book provides a systematic and comprehensive introduction to the theory and practice of mathematical modelling, covering both deterministic and stochastic models, linear and nonlinear models, discrete and continuous models, and deterministic and probabilistic models.
The book also presents numerous examples and applications of mathematical modelling in various domains, such as population dynamics, epidemiology, ecology, genetics, thermodynamics, chemical kinetics, fluid mechanics, electrical circuits, control systems, optimization, game theory, cryptography, and more.
The book is suitable for undergraduate and graduate students of mathematics, physics, engineering, computer science, and other related disciplines. It is also a valuable reference for researchers and practitioners who use mathematical modelling in their work.
If you are interested in learning more about mathematical modelling and its applications, you can download a free PDF version of Mathematical Modelling by J.N. Kapur from the Internet Archive . You can also buy a hardcover or paperback edition of the book from Google Books or other online retailers.
Mathematical modelling is not only a theoretical endeavour, but also a practical one. It can help us understand complex systems, predict their behaviour, design optimal solutions, and test hypotheses. Mathematical modelling can also help us communicate our ideas and findings to others, using clear and precise language.
However, mathematical modelling also poses some challenges and limitations. It requires creativity, intuition, and critical thinking to formulate appropriate models that capture the essential features of the problem. It also requires mathematical skills and computational tools to analyze and solve the models. Moreover, it requires validation and verification to ensure that the models are consistent with the data and the reality.
Therefore, mathematical modelling is both an art and a science. It is a process of abstraction, simplification, generalization, and approximation. It is also a process of exploration, experimentation, discovery, and innovation. Mathematical modelling is a rewarding and fascinating activity that can enrich our knowledge and expand our horizons.
In this article, we have introduced the concept and scope of mathematical modelling, and discussed some of the benefits and challenges of this technique. We have also reviewed one of the most influential books on mathematical modelling, Mathematical Modelling by J.N. Kapur, which provides a comprehensive and systematic exposition of the theory and practice of mathematical modelling.
If you want to learn more about mathematical modelling and its applications, we recommend you to read this book and try some of the exercises and examples. You can also explore other books and online resources on mathematical modelling, such as:
- Mathematical Modeling by Mark M. Meerschaert, which covers a wide range of topics and applications in mathematical modelling, such as differential equations, discrete models, optimization, simulation, stochastic models, and more.
- Mathematical Modelling: A Case Studies Approach by Reinhard Illner et al., which presents a collection of case studies that illustrate the use of mathematical modelling in various fields, such as biology, ecology, epidemiology, physics, chemistry, engineering, economics, and more.
- Mathematical Modeling: The Art of Translating Problems into Mathematics by William P. Fox, which focuses on the process of translating real-world problems into mathematical models, using examples from engineering, science, business, and social sciences.
- Mathematical Modeling with Excel by Brian Albright, which introduces the basics of mathematical modelling using Excel as a tool for data analysis, visualization, and simulation.
We hope you have enjoyed this article and learned something new about mathematical modelling. We encourage you to try mathematical modelling yourself and see how it can help you solve problems and discover new insights.