Overview
- The topics of tensors and differential geometry are presented in a comprehensive and approachable way
- With worked-out examples and concrete calculations
- The reader is carefully guided to advanced topics
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Engineering (MATHENGIN)
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Table of contents (4 chapters)
Keywords
- Bra and Ket Notation
- 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
About this book
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics and cybernetics.
This book comprehensively presents topics, such as bra-ket notation, tensor analysis and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. 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 and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists and practicing engineers.
Reviews
“The book begins by introducing the concepts general basis and tensor types for curvilinear coordinates … . The mathematics is presented with clarity and precision. In particular, I like the way in which concepts are illustrated in the context of low dimensional cases, and the narrative is interspersed with many informative illustrations. In other words, it’s the sort of book that attracts one’s attention on a first perusal.” (Peter Ruane, MAA Reviews, April, 2015)
Authors and Affiliations
About the authors
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).
Bibliographic Information
Book Title: Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers
Authors: Hung Nguyen-Schäfer, Jan-Philip Schmidt
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-662-43444-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
eBook ISBN: 978-3-662-43444-4Published: 01 July 2014
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XIII, 241
Number of Illustrations: 50 b/w illustrations
Topics: Mathematical and Computational Engineering, Mathematical Methods in Physics, Computational Science and Engineering, Solid Mechanics