Tensor Analysis and Its Applications
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The object of this book is to provide a compact exposition of the fundamental results in the theory of tensors and also to illustrate the power of the tensor technique by applications to differential geometry, elasticity, and relativity. This book is intended to be a textbook, suitable for use in a undergraduate / postgraduate Mathematics course. This book is useful for those who are totally unfamiliar with tensor analysis. Those who are already acquainted with tensor analysis will fell interested in application of tensor analysis in Riemannian geometry, theory of relativity and many other disciplines of science and technology. This book consists of six chapters. In which we have discuss tensors and its operations,Christoffel’s symbols, covariant differentiation of tensors, Riemann’s symbols , flat space, Einstein space.
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About the Book
This book is intended to serve as a textbook for undergraduate and postgraduate students of mathematics. It will be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and other higher education tests. The text starts with the basic concepts and results, which shall refer throughout this book and is followed by the study of the tensor algebra and its calculus, consisting the notion of tensor, its operations, and its different types; Christoffel’s symbols and its properties, the concept of covariant differentiation of tensors and its properties, tensor form of gradient, divergence, laplacian and curl, divergence of a tensor, intrinsic derivatives, and parallel displacement of vectors, Riemann’s symbols and its properties, and application of tensor in different areas.
About the Author
Dr. Quddus Khan, PhD, is a senior associate professor in the Department of Applied Science and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India. He has been teaching undergraduate and postgraduate classes for the last sixteen years. Dr. Khan has to his credit sixteen research papers published in various national and international journals and has coauthored three books, authored three books, and produced two PhDs.