EAN: 9783319127866

UNDERGRADUATE LECTURE NOTES IN PHYSICS TENSOR...

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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