Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Derivatives of Vectors and Tensors

  • L. P. Lebedev
  • M. J. Cloud
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_215-1

Synonyms

Definitions

A tensor field is a tensor-valued function of position in space. Hence a scalar field is a mapping that assigns a scalar to each point of some domain in \(\mathbb R^3\)

This is a preview of subscription content, log in to check access.

References

  1. Danielson D (2003) Vectors and tensors in engineering and physics. Westview Press, BoulderGoogle Scholar
  2. Dmitrienko Y (2002) Tensor analysis and nonlinear tensor functions. Springer, New YorkGoogle Scholar
  3. Filho E (2016) Tensor calculus for engineers and physicists. Springer, New YorkGoogle Scholar
  4. Itskov M (2015) Tensor algebra and tensor analysis for engineers: with applications to continuum mechanics. Springer, New YorkGoogle Scholar
  5. Lebedev L, Cloud M, Eremeyev V (2010) Tensor analysis with applications in mechanics. World Scientific, SingaporeGoogle Scholar
  6. Lurie A (2005) Theory of elasticity. Springer, New YorkGoogle Scholar
  7. Lurie A (2012) Non-linear theory of elasticity. North Holland, AmsterdamGoogle Scholar
  8. Simmonds J (1997) A brief on tensor analysis. Springer, New YorkGoogle Scholar
  9. Zhilin P (2001) Vectors and second-rank tensors in three-dimensional space. Nestor, St. Petersburg (in Russian)Google Scholar
  10. Zubov L, Karyakin M (2006) Tensor calculus: basic theory. University Books, Moscow (in Russian)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.National University of ColombiaBogotaColombia
  2. 2.Department of Electrical and Computer EngineeringLawrence Technological UniversitySouthfieldUSA

Section editors and affiliations

  • Leonid P. Lebedev
    • 1
  • Michael J. Cloud
    • 2
  1. 1.Universidad Nacional de ColombiaBogotá D.C.Colombia
  2. 2.Department of Electrical and Computer EngineeringLawrence Technological UniversitySouthfieldUSA