Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

• Hung Nguyen-Schäfer
• Jan-Philip Schmidt
Book

Part of the Mathematical Engineering book series (MATHENGIN)

1. Front Matter
Pages i-xvii
2. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 1-34
3. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 35-101
4. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 103-154
5. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 155-180
6. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 181-247
7. Hung Nguyen-Schäfer, Jan-Philip Schmidt
Pages 249-311
8. Back Matter
Pages 313-376

Introduction

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.

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

Authors and affiliations

• Hung Nguyen-Schäfer
• 1
• Jan-Philip Schmidt
• 2
1. 1.EM-motive GmbHLudwigsburgGermany
2. 2.Interdisciplinary Center for Science Computing (IWR)University of Heidelberg HeidelbergGermany

Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-48497-5
• Copyright Information Springer-Verlag Berlin Heidelberg 2017
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-662-48495-1
• Online ISBN 978-3-662-48497-5
• Series Print ISSN 2192-4732
• Series Online ISSN 2192-4740
• Buy this book on publisher's site
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