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In mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type. Raising and lowering indices are a form of index manipulation in tensor expressions.
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". 1. List of mathematical topics in classical mechanics; List of mathematical topics in quantum theory
The index of a vector field is an integer that helps describe its behaviour around an isolated zero (i.e., an isolated singularity of the field). In the plane, the index takes the value −1 at a saddle singularity but +1 at a source or sink singularity. Let n be the dimension of the manifold on which the vector field is defined. Take a closed ...
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
This glossary of physics is a list of definitions of terms and concepts relevant to physics, ... (mathematics) 2. (physics) particle ... refractive index
kilogram meter squared (kg⋅m 2) intensity: watt per square meter (W/m 2) imaginary unit: unitless electric current: ampere (A) ^ Cartesian x-axis basis unit vector unitless current density: ampere per square meter (A/m 2) impulse: kilogram meter per second (kg⋅m/s)
There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science.
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.