Tensor Analysis and Its Applications

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.