Tensor analysis and elementary differential geometry for physicists and engineers

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This book presents tensors and differential geometry in a comprehensive and accessible way, bridging the gap between physics and engineering mathematics and tensor analysis. It covers topics such as tensor analysis, the elementary differential geometry of moving surfaces, and k-differential forms. With numerous examples and solutions, the text guides readers through complex concepts step by step. Prioritizing practicality for engineers and physicists, it favors simplicity over a rigorous approach. The book demonstrates how to work with tensors and differential geometry and apply them to modeling in the physical and engineering realms. Key areas of focus include: General Basis and Bra-Ket Notation, Tensor Analysis, Elementary Differential Geometry, Differential Forms, and their applications in quantum mechanics. The text also reviews methods in computational fluid dynamics, continuum mechanics, electrodynamics in special relativity, cosmology in Minkowski space-time, and both relativistic and non-relativistic quantum mechanics. This resource is valuable for research scientists and practicing engineers across various fields who utilize tensor analysis and differential geometry in applied physics, as well as for graduate students in applied physics and engineering.