Mathematical modelling of systems and analysis
/ K. Kamalanand, P. Mannar Jawahar
. — Delhi : PHI Learning, 2019.
252 p.
Description:
This book is written with the ideology of providing a simple yet concise explanation on the art of developing mathematical models. This lively and engaging text explicates the basics of mathematical modelling, with special focus on its applications and analysis.
Organised in thirteen chapters, the book emphasises the theory and classification of systems, modelling using ordinary differential equations, calculus of variations, stability analysis, system identification and parameter estimation techniques. Also, it includes examples from the areas of mechanics, chemical reactions, biology, population dynamics, epidemiology, and other allied fields of science, engineering and technology.
This book is primarily designed for the postgraduate students of mathematics as well as for the undergraduate and postgraduate engineering students of various disciplines for their paper on Modelling and Simulation/Mathematical Modelling and Simulation/Mathematical Modelling.
KEY FEATURES
• Inclusion of entropy-based modelling, modelling using fractional order ODEs and artificial intelligence along with stability and catastrophe theory is the major highlight of this book.
• Figures and tables well support the text.
• Numerous worked-out examples make the students aware of problem-solving methodology.
• Chapter-end exercises help the students from practice point of view.
• References and suggested reading at the end of the book broaden its scope.
KAMALANAND, K. K. KAMALANAND, Ph.D., is Assistant Professor in the Department of Instrumentation Engineering at Madras Institute of Technology Campus, Anna University, Chennai. His research focuses on mathematical modelling and analysis of physical and biological systems. He has authored several papers and book chapters. Dr. Kamalanand is also an Editor for Computational Techniques for Dental Image Analysis, and a Guest Editor for the European Journal for Biomedical Informatics, Current Bioinformatics and Current Signal Transduction Therapy.
JAWAHAR, P. MANNAR P. MANNAR JAWAHAR, Ph.D., is Vice Chancellor, Karunya Institute of Technology and Sciences. He completed his Ph.D. from IIT Delhi and subsequently did his Post Doctoral Research work from Warsaw University of Technology, Poland. He joined Anna University as a Faculty in 1978 and has put in more than three decades of service in teaching profession. He served as the Vice Chancellor of Anna University from June 2008 to June 2012. His current research interest includes the application of computational methods in biomedical analysis..
Preface Chapter 1: Introduction to Theory of Systems Chapter 2: Classification and Representations of Systems Chapter 3: Mathematical Modelling of Systems Chapter 4: Representation a Family of Curves Using Ordinary Differential Equations Chapter 5: System Modelling Using Difference Equations and Ordinary Differential Equations Chapter 6: Mathematical Modelling Using Balance Laws Chapter 7: Mathematical Modelling of Chemical Reactions Chapter 8: Mathematical Modelling of Population Dynamics Chapter 9: Mathematical Modelling Using The Calculus of Variations Chapter 10: Stability Theory Chapter 11: State Space Models and Transfer Functions Chapter 12: System Identification Chapter 13: Parameter Estimation Techniques References • Further Reading • Index
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