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exponential solution

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  • Exponential integral — is a mathematical function of a single argument which has no established notation.DefinitionsFor real values of x , the exponential integral Ei( x ) can be defined as : mbox{Ei}(x)=int { infty}^xfrac{e^t}t,dt., The definition above can be used… …   Wikipedia

  • Exponential decay — A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constants of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is said to be subject to exponential… …   Wikipedia

  • Exponential function — The natural exponential function y = ex In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative …   Wikipedia

  • Exponential map — In differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis to all differentiable manifolds with an affine connection. Two important special cases of this are the exponential map …   Wikipedia

  • Exponential growth — The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.   Exponential growth …   Wikipedia

  • Exponential dichotomy — In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non autonomous systems.DefinitionIf:dotmathbf{x} = A(t)mathbf{x}is a linear non autonomous… …   Wikipedia

  • Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… …   Wikipedia

  • Doléans-Dade exponential — In stochastic calculus, the Doléans Dade exponential, Doléans exponential, or stochastic exponential, of a semimartingale X is defined to be the solution to the stochastic differential equation dYt = Yt dXt with initial condition Y0 = 1. The… …   Wikipedia

  • Tarski's exponential function problem — In model theory, Tarski s exponential function problem asks whether the usual theory of the real numbers together with the exponential function is decidable. Tarski had previously shown that the theory of the real numbers (without the exponential …   Wikipedia

  • Characterizations of the exponential function — In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent …   Wikipedia

  • Ordered exponential — The ordered exponential (also called the path ordered exponential) is a mathematical object, defined in non commutative algebras, which is equivalent to the exponential function of the integral in the commutative algebras. Therefore it is a… …   Wikipedia

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