Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers (eBook)

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2016 | 2nd ed. 2017
XVII, 376 Seiten
Springer Berlin (Verlag)
978-3-662-48497-5 (ISBN)

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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers - Hung Nguyen-Schäfer, Jan-Philip Schmidt
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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.



Dr. Hung Nguyen-Schäfer is a senior technical manager in development of electric machines for hybrid and electric vehicles at EM-motive GmbH, a joint company of Daimler and Bosch in Germany. He received B.Sc. and M.Sc. in mechanical engineering with nonlinear vibrations in fluid mechanics from the University of Karlsruhe (KIT), Germany in 1985; and a Ph.D. degree in nonlinear thermo- and fluid dynamics from the same university in 1989. He joined Bosch Company and worked as a technical manager on many development projects. Between 2007 and 2013, he was in charge of rotordynamics, bearings and design platforms of automotive turbochargers at Bosch Mahle Turbo Systems in Stuttgart.

He is also the author of two professional engineering books: Rotordynamics of Automotive Turbochargers, Springer (2012) and Aero and Vibroacoustics of Automotive Turbochargers, Springer (2013). 

Rotordynamics of Automotive Turbochargers, Springer (2012) and Aero and Vibroacoustics of Automotive Turbochargers, Springer (2013).

Dr. Jan-Philip Schmidt is a mathematician. He studied mathematics, physics, and economics at the University of Heidelberg, Germany. He received a Ph.D. degree in mathematics from the University of Heidelberg in 2012. His doctoral thesis was funded by a research fellowship from the Heidelberg Academy of Sciences, in collaboration with the Interdisciplinary Center for Scientific Computing (IWR) at the University of Heidelberg. His academic working experience comprises several research visits in France and Israel, as well as project works at the Max-Planck-Institute for Mathematics in the Sciences (MPIMIS) in Leipzig, and at the Max-Planck-Institute for Molecular Genetics (MPIMG) in Berlin. He also worked as a research associate in the AVACS program at Saarland University, Cluster of Excellence (MMCI).

Dr. Hung Nguyen-Schäfer is a senior technical manager in development of electric machines for hybrid and electric vehicles at EM-motive GmbH, a joint company of Daimler and Bosch in Germany. He received B.Sc. and M.Sc. in mechanical engineering with nonlinear vibrations in fluid mechanics from the University of Karlsruhe (KIT), Germany in 1985; and a Ph.D. degree in nonlinear thermo- and fluid dynamics from the same university in 1989. He joined Bosch Company and worked as a technical manager on many development projects. Between 2007 and 2013, he was in charge of rotordynamics, bearings and design platforms of automotive turbochargers at Bosch Mahle Turbo Systems in Stuttgart.He is also the author of two professional engineering books: Rotordynamics of Automotive Turbochargers, Springer (2012) and Aero and Vibroacoustics of Automotive Turbochargers, Springer (2013). Rotordynamics of Automotive Turbochargers, Springer (2012) and Aero and Vibroacoustics of Automotive Turbochargers, Springer (2013).Dr. Jan-Philip Schmidt is a mathematician. He studied mathematics, physics, and economics at the University of Heidelberg, Germany. He received a Ph.D. degree in mathematics from the University of Heidelberg in 2012. His doctoral thesis was funded by a research fellowship from the Heidelberg Academy of Sciences, in collaboration with the Interdisciplinary Center for Scientific Computing (IWR) at the University of Heidelberg. His academic working experience comprises several research visits in France and Israel, as well as project works at the Max-Planck-Institute for Mathematics in the Sciences (MPIMIS) in Leipzig, and at the Max-Planck-Institute for Molecular Genetics (MPIMG) in Berlin. He also worked as a research associate in the AVACS program at Saarland University, Cluster of Excellence (MMCI).

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.

Erscheint lt. Verlag 16.8.2016
Reihe/Serie Mathematical Engineering
Mathematical Engineering
Zusatzinfo XVII, 376 p. 73 illus.
Verlagsort Berlin
Sprache englisch
Themenwelt Mathematik / Informatik Informatik
Mathematik / Informatik Mathematik
Naturwissenschaften Physik / Astronomie
Technik Maschinenbau
Schlagworte Bra and Ket Notation • Bra–ket notation • Computational Fluid Dynamics (CFD) • Differential Geometry with a Moving Surface • Dirac notation • elementary differential geometry • Euclidean and Riemannian Manifolds • Lie derivatives • Maxwell’s Equations in Relativity Field Theories • Maxwell’s Equations in Relativity Field Theories • navier-stokes equations • Surface curvatures • Tensor Analysis • Transformations of Curvilinear Coordinates
ISBN-10 3-662-48497-8 / 3662484978
ISBN-13 978-3-662-48497-5 / 9783662484975
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