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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Part of the Mathematical Engineering Book Series (volume 21)

DOI: 10.1007/978-3-662-43444-4

ISBN: 978-3-662-43443-7

Publisher: Springer Berlin Heidelberg - Springer Journals

Jul 2, 2014

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Chapter 1General Basis and Bra–Ket Notation

Nguyen-Schäfer, Hung; Schmidt, Jan-Philip

Pages: 1 –34

[We begin this chapter by reviewing some mathematical backgrounds dealing with coordinate transformations and general basis vectors in general curvilinear coordinates. Some of these aspects will be informally discussed for the sake of simplicity. Therefore, those readers interested in more...
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Chapter 2Tensor Analysis

Nguyen-Schäfer, Hung; Schmidt, Jan-Philip

Pages: 35 –99

[Tensors are a powerful mathematical tool that is used in many areas in engineering and physics including general relativity theory, quantum mechanics, statistical thermodynamics, classical mechanics, electrodynamics, solid mechanics, and fluid dynamics. Laws of physics and physical invariants...
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Chapter 3Elementary Differential Geometry

Nguyen-Schäfer, Hung; Schmidt, Jan-Philip

Pages: 101 –142

[We consider an N-dimensional Riemannian manifold M, and let gi be a basis at the point Pi(u1, …, uN) and gj be another basis at the other point Pj(u1, …,uN). Note that each such basis may only exist in a local neighborhood of the respective points and not necessarily for the whole space. For...
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Chapter 4Applications of Tensors and Differential Geometry

Nguyen-Schäfer, Hung; Schmidt, Jan-Philip

Pages: 143 –196

[Nabla operator is a linear map of an arbitrary tensor into an image tensor in N-dimensional curvilinear coordinates.]

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