Tensors for physics [electronic resource]

• 作者： Hess, Siegfried.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Undergraduate lecture notes in physics
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Undergraduate lecture notes in physics
• 主題： Calculus of tensors , Mathematical physics , Physics , Mathematical Methods in Physics. , Mathematical Applications in the Physical Sciences. , Soft and Granular Matter, Complex Fluids and Microfluidics. , Physical Chemistry. , Appl.Mathematics/Computational Methods of Engineering.
• ISBN： 9783319127873 (electronic bk.) 、 9783319127866 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- Basics -- Symmetry of Second Rank Tensors, Cross Product -- Epsilon-Tensor -- Symmetric Second Rank Tensors -- Summary: Decomposition of Second Rank Tensors -- Fields, Spatial Differential Operators -- Integration of Fields -- Irreducible Tensors -- Multiple Potentials -- Isotropic Tensors -- Integral Formulae -- Spin Operators -- Rotation of Tensors -- Liquid Crystals -- Constitutive Relations -- Tensor Dynamics -- Maxwell Equations, from 3D to 4D -- Exercises: Answers and Solutions.
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• 摘要註: This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.
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