© 2014

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers


  • 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


Part of the Mathematical Engineering book series (MATHENGIN, volume 21)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Hung Nguyen-Schäfer, Jan-Philip Schmidt
    Pages 1-34
  3. Hung Nguyen-Schäfer, Jan-Philip Schmidt
    Pages 35-99
  4. Hung Nguyen-Schäfer, Jan-Philip Schmidt
    Pages 101-142
  5. Hung Nguyen-Schäfer, Jan-Philip Schmidt
    Pages 143-196
  6. Back Matter
    Pages 197-241

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.


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

Authors and affiliations

  1. 1.EM-motive GmbH (A Joint Company of Daimler and Bosch)LudwigsburgGermany
  2. 2.Interdisciplinary Center for ScientificUniversity of HeidelbergHeidelbergGermany

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

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“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)