Tensor Calculus and Applications
Simplified Tools and Techniques
The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject -tensor, and can be used in many fields of research. Special applications are discussed in the book, to remove any confusion, and for absolute understanding of the subject.
In most books, they emphasize only the theoretical development, but not the methods of presentation, to develop concepts. Without knowing how to change the dummy indices, or the real indices, the concept cannot be understood. This book takes it down a notch and simplifies the topic for easy comprehension.
- Provides a clear indication and understanding of the subject on how to change indices
- Describes the original evolution of symbols necessary for tensors
- Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems
- Presents the correlation between critical concepts
- Covers general operations and concepts
Table of Contents
Part I Formalism of Tensor Calculus. 1. Prerequisites for Tensors. 2. Concept of Tensors. 3. Riemannian Metric and Fundamental Tensors. 4. Christoffel Three-Index Symbols (Brackets) and Covariant Differentiation. 5. Properties of Curves in Vn and Geodesics. 6. Riemann Symbols (Curvature Tensors). Part II. Application of Tensors. 7. Applications of Tensors in General Theory of Relativity. 8. Tensors in Continuum Mechanics. 9. Tensors in Geology. 10. Tensors in Fluid Dynamics. Appendix. Remarks. Bibliography.
Dr. Bhaben Chandra Kalita, has been first Class throughout the career. He has served 37 years in the department of Mathematics, Gauhati University in the capacity of Assistant and Associate professors and professor head of the Department since 1978. Dr. Kalita was granted the prestigious award "Professor Emeritus" by the University Grants Commission (UGC), Govt. of India on Sept, 2015. He has published about 50 (fifty) papers in Physics of Fluids, Phys. of Plasmas, Astrophysics and Space Science, Journal of Plasma Physics, Physical Society of Japan, Canadian Journal of Physics, Transaction on Plasma science, IEEE, and Commun. In Theoretical Physics, Plasma Physics Reports, besides some other papers of Relativity and Graph Theory. He has acted as invited speaker in Astrophysics and Particle Physics in Dalas (2016), San Antonio (2017). He has presented Papers in Granada (Spain), Pissa (Italy), Swansea (UK), and acted as speaker in many local Universities and Institutions. Authored several text books on Advanced Mathematics and reference books of Higher Secondary Level.