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 examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book.
This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.
Zafar Ahsan, Ph.D., is a Professor at the Department of Mathematics, Aligarh Muslim University, Aligarh, India. He is Editor-in-Chief of Journal of Tensor Society of India (2010-2012), Managing Editor of Aligarh Bulletin of Mathematics (1998-2012); Editor, Palestian Journal of Mathematics, Editor, Journal of Interpolation and Approximation in Scientific Computing. Member of Editorial Boards of Global Journal of Advanced Research on Classical and Modern Geometries, Taif Journal of Mathematics and Statistics, Journal of Tensor Society and Journal of Calcutta Mathematical Society; Referee of various journals of mathematics and physics. Prof. Ahsan has been a Council Member of Indian Association for General Relativity and Gravitation (2002-2006); a Visiting Associate of Inter University Centre of Astronomy and Astrophysics (IUCAA), Pune (July 1996-June 2005) and a UGC Visiting Professor of Sardar Patel University, Vallabh Vidyanagar (April 2004-May 2005). He is also life member of Indian Association for General Relativity and Gravitation, Calcutta Mathematical Society, Indian Society of Industrial and Applied Mathematics, Indian Mathematical Society and Tensor Society of India. Professor Zafar Ahsan has published 96 research papers in national and international journals of repute and has authored three books. His areas of research interest include General Relativity, Gravitation and The Quran and Modern Cosmology.