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- In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.
- When more specific types of differentiation are necessary, such as in multivariate calculus or tensor analysis, other notations are common.
- There he studied the mathematical tools of the general theory of relativity and conceived his method for applying tensor analysis to electrical power engineering.
- Dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis with finite-dimensional vector spaces.
- He wrote "Der Ricci-Kalkül" in 1922 surveying the field of tensor analysis.
- The works of physicists such as James Clerk Maxwell, and mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita led to the development of tensor analysis and the notion of covariance, which identifies an intrinsic geometric property as one that is invariant with respect to coordinate transformations.
- The Tensor Society of Great Britain came into being to further the understanding and applications of tensor analysis."
- Simmonds, in his book on tensor analysis, quotes Albert Einstein saying in examining the invariance properties of Maxwell's equations which has been of interest in metamaterials Green and Zerna, Basar and Weichert, and Ciarlet.
- Chebotarev believed that the tensor analysis is necessary for them.
- NEL explored transducer theory with tensor analysis and continuum mechanics to determine viscous and hysteretic dissipative effects of transducer materials and radiation impedance of transducers in the water medium.
- By using Cartesian tensor notation in his last three books, "Engineering Mechanics", "Statics of Deformable Bodies", and "Cartesian Tensors", Myklestad became an early proponent of tensor analysis in the undergraduate engineering curriculum.
- In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
- This culminated in 1910 with the publication of Woldemar Voigt's "Lehrbuch der Kristallphysik" ("Textbook on Crystal Physics"), which described the 20 natural crystal classes capable of piezoelectricity, and rigorously defined the piezoelectric constants using tensor analysis.
- Simmonds, in his book on tensor analysis, quotes Albert Einstein saying in examining the invariance properties of Maxwell's equations which has been of interest in metamaterials Simmonds, Green and Zerna, Basar and Weichert, and Ciarlet.
- During 1946 the department is noted as having taught advanced analytics, geometry, and tensor analysis.
- In tensor analysis, superscripts are used instead of subscripts to distinguish covariant from contravariant entities, see covariance and contravariance of vectors and raising and lowering indices.
- In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript (contravariant).
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