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In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves: = = (+) (^ ^), where i is the imaginary unit , k is a wave vector of length k ,
Linear Operators is a three-volume textbook on the theory of linear operators, written by Nelson Dunford and Jacob T. Schwartz. The three volumes are (I) General Theory; (II) Spectral Theory, Self Adjoint Operators in Hilbert Space; and (III) Spectral Operators. The first volume was published in 1958, the second in 1963, and the third in 1971.
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems , linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems . [ 1 ]
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number < such that for all x and y in M,
The application of linear algebra in this context is vital for the design and operation of modern power systems, including renewable energy sources and smart grids. Overall, the application of linear algebra in fluid mechanics, fluid dynamics, and thermal energy systems is an example of the profound interconnection between mathematics and ...
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature.For a property R that changes when the temperature changes by dT, the temperature coefficient α is defined by the following equation:
Growth of the eight largest Wikibooks sites (by language), July 2003–January 2010. Wikibooks (previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks) is a wiki-based Wikimedia project hosted by the Wikimedia Foundation for the creation of free content digital textbooks and annotated texts that anyone can edit.