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.
The aim of Mechano-Electric Correlations in the Human Physiological System is to present the mechanical and electrical properties of human soft tissues and the mathematical models related to the evaluation of these properties in time, as well as their biomedical applications. This book also provides an overview of the bioelectric signals of soft tissues from various parts of the human body. In addition, this book presents the basic dielectric and viscoelastic characteristics of soft tissues, an introduction to the measurement and characteristics of bioelectric signals and their relationship with the mechanical activity, electromyography and the correlation of electromyograms with the muscle activity in normal and certain clinical conditions. The authors also present a case study on the effect of lymphatic filariasis on the mechanical and electrical activity of the muscle. Features: Explains the basics of electrical and mechanical properties of soft tissues in time and frequency domain along with the mathematical models of soft tissue mechanics Explores the correlation of electrical properties with the mechanical properties of biological soft tissues using computational techniques Provides a detailed introduction to electrophysiological signals along with the types, applications, properties, problems and associated mathematical models Explains the electromechanics of muscles using electromyography recordings from various muscles of the human physiological system Presents a case study on the effect of lymphatic filariasis on the mechanical and electrical activity of the muscle Mechano-Electric Correlations in the Human Physiological System is intended for biomedical engineers, researchers and medical scientists as well graduate and undergraduate students working on the mechanical properties of soft tissues.
The aim of this book is to outline the concept of entropy, various types of entropies and their implementation to evaluate a variety of biomedical signals/images. The book emphasizes various entropy-based image pre-processing methods which are essential for the development of suitable computerized examination systems. The recent research works on biomedical signal evaluation confirms that signal analysis provides vital information regarding the physiological condition of the patient, and the efficient evaluation of these signals can help to diagnose the nature and the severity of the disease. This book emphasizes various entropy-based image pre-processing methods which are essential for the development of suitable computerized examination systems for the analysis of biomedical images recorded with a variety of modalities. The work discusses the image pro-processing methods with the Entropies, such as Kapur, Tsallis, Shannon and Fuzzy on a class of RGB-scaled and gray-scaled medical pictures. The performance of the proposed technique is justified with the help of suitable case studies, which involves x-ray image analysis, MRI analysis and CT analysis. This book is intended for medical signal/image analysts, undergraduate and postgraduate students, researchers, and medical scientists interested in biomedical data evaluation.
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