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This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins.
Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world.
The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering:
-General Basis and Bra-Ket Notation
-Tensor Analysis
-Elementary Differential Geometry
-Differential Forms
-Applications of Tensors and Differential Geometry
-Tensors and Bra-Ket Notation in Quantum Mechanics
The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics.
Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Table des matières
General Basis and Bra-Ket Notation.- Tensor Analysis.- Elementary Differential Geometry.- Differential Forms.- Applications of Tensors and Differential Geometry.- Tensors and Bra-Ket Notation in Quantum Mechanics.- Appendices.
A propos de l'auteur
Dr. Hung Nguyen-Schaefer is a senior expert in rotor-dynamics and bearing designs of turbochargers at Bosch Mahle Turbo Systems (BMTS) in Germany. He received his B.Sc. and M.Sc. in mechanical engineering with nonlinear vibrations in fluid mechanics from the University of Karlsruhe, Germany in 1985, and his Ph.D. in nonlinear thermo- and fluid dynamics from the same university. In 1988 he joined Bosch company, and worked as technical manager on many development projects of anti-lock braking and traction systems, high-pressure fuel injection systems, combustion engine systems, fluid cavitation, and electric turbochargers for automotive fuel cells (PEMFC). Since 2007 Dr. Nguyen-Schaefer has been in charge of rotordynamics and bearing design of automotive turbochargers at BMTS located in Stuttgart, the joint venture of Bosch and Mahle. He has much experience in the fuel injection systems of gasoline, diesel, compressed natural gas (CNG), automotive turbochargers, rotordynamics, and bearing designs.
Résumé
This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world.The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation• Tensor Analysis• Elementary Differential Geometry• Differential Forms• Applications of Tensors and Differential Geometry• Tensors and Bra-Ket Notation in Quantum MechanicsThe text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics.Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Texte suppl.
“The overall impression of the book is positive. Being addressed to physicists and engineers, it succeeds to impart a fairly sound knowledge of differential geometry and its instruments – the tensors – and show how this theory can be fruitfully applied.” (Eleutherius Symeonidis, zbMATH 1369.53002, 2017)
“This book is an excellent systematic realization of tensor analysis for engineers and physicists at all levels, from undergraduate students to experts.” (Hamid R. Noori, Computing Reviews, September, 2015)
Commentaire
"The overall impression of the book is positive. Being addressed to physicists and engineers, it succeeds to impart a fairly sound knowledge of differential geometry and its instruments - the tensors - and show how this theory can be fruitfully applied." (Eleutherius Symeonidis, zbMATH 1369.53002, 2017)
"This book is an excellent systematic realization of tensor analysis for engineers and physicists at all levels, from undergraduate students to experts." (Hamid R. Noori, Computing Reviews, September, 2015)
