Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Beschreibung

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics.

Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum mechanics, cosmology, electrodynamics, computational fluid dynamics (CFD), and continuum mechanics.
The target audience of this all-in-one book primarily comprises graduate students in mathematics, physics, engineering, research scientists, and engineers.     

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.
Presents advanced mathematical topics in an approachable fashion Works step by step through numerous examples with solutions and concrete calculations A survey of tensor analysis and differential geometry, geared to physicists and engineers

Autor*in

Hung Nguyen-Schäfer

Themen in »Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers«

Computational Fluid Dynamics (CFD) Differential Geometry with a Moving Surface Euclidean and Riemannian Manifolds Lie Derivatives Maxwell’s Equations in Relativity Field Theories Navier-Stokes Equations Surface Curvatures Tensor Analysis Transformations of Curvilinear Coordinates Bra–ket notation Dirac notation elementary differential geometry

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“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)

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