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DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
Primarily intended for the undergraduate students of mathematics, physics and engineering, this text gives in-depth coverage of differential equations and the methods for solving them. The book begins with the definitions, the physical and geometric origins of differential equations, and the methods for solving the first order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher order differential equations and their applications to telecommunications, civil engineering, cardiology and detection of diabetes, as also the...
DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
Primarily intended for the undergraduate students in Mathematics, Physics and Engineering, this text gives in-depth coverage of differential equations and the methods of solving them. The book begins with the basic definitions, the physical and geometric origins of differential equations, and the methods for solving first-order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher-order differential equations and their applications to telecom-munications, civil engineering, cardiology and detec-tion of diabetes, as also the methods of solving simultaneous differential equations and their applica-tions. Besides, the book provides a detailed discussion on Laplace transform and their applications, partial differential equations and their applications to vibration of a stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. This book, which is a happy fusion of theory and application, would also be useful to postgraduate students.
Advanced Calculus
This concise and systematically organized textbook is meant for the undergraduate students of engineering for their courses in Engineering Mathematics. Besides, it is also useful for undergraduate and postgraduate students of mathematics. This book is divided into nine chapters; the initial chapters provide revision of fundamental concepts of functions, limits and continuity to help students grasp the idea of the derivations treated in the subsequent chapters. Rules for finding derivatives, Taylor’s and Maclaurin’s theorems and different types of indeterminate forms are thoroughly explained. Further the book covers the convergence and divergence of the series, tangents and normals, curvatures to the curves, maxima and minima of functions of more than one variables and directional derivatives. The text also deals with volume integrals, and concludes with a detailed discussion on the line integrals and surface integrals using divergence and Stokes’ theorems.
TENSORS
The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved exam...
The Potential of Fields in Einstein's Theory of Gravitation
This book presents a detailed study of the Lanczos potential in general relativity by using tetrad formalisms. It demonstrates that these formalisms offer some simplifications over the tensorial methods, and investigates a general approach to finding the Lanczos potential for algebraic space–time by translating all the tensorial relations concerning the Lanczos potential into the language of tetrad formalisms and using the Newman–Penrose and Geroch–Held–Penrose formalisms. In addition, the book obtains the Lanczos potential for perfect fluid space–time, and applies the results to cosmological models of the universe. In closing, it highlights other methods, apart from tetrad formalisms, for finding the Lanczos potential, as well as further applications of the Newman–Penrose formalism. Given its scope, the book will be of interest to pure mathematicians, theoretical physicists and cosmologists, and will provide common ground for communication among these scientific communities.
Recent Advances in Differential Equations and its Applications (DEAPP–2017)
Differential Equations serve as mathematical models for virtually any natural or physical phenomena in science and technology and has applications even in diverse fields such as economics, medicine, ecology, etc. The seminar was organized to throw light on the recent advances in the applications of differential equations and to provide a platform for sharing the knowledge with experts in the field with young students and researchers. The Researchers and educators in the field of differential equations were invited to attend and share their rich experience. As for everything else. so for a mathematical theory. beauty can be perceived but not explained.
The King and the People
An original exploration of the relationship between the Mughal emperor and his subjects in the space of the Mughal empire's capital, The King and the People overturns an axiomatic assumption in the history of premodern South Asia: that the urban masses were merely passive objects of rule and remained unable to express collective political aspirations until the coming of colonialism. Set in the Mughal capital of Shahjahanabad (Delhi) from its founding to Nadir Shah's devastating invasion of 1739, this book instead shows how the trends and events in the second half of the seventeenth century inadvertently set the stage for the emergence of the people as actors in a regime which saw them only a...
Sufi Women of South Asia
In Sufi Women of South Asia. Veiled Friends of God, Tahera Aftab, drawing upon various sources, offers the first unique and comprehensive account of South Asian Sufi women, from the eleventh to the twentieth century.
Courting Constitutionalism
Presents a deeply contextualized account of public law and judicial review in Pakistan.
INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION
This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem...
