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System of equations information


In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:

  • System of linear equations,
  • System of nonlinear equations,
  • System of bilinear equations,
  • System of polynomial equations,
  • System of differential equations, or a
  • System of difference equations

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System of equations

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equation system is usually classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations,...

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System of linear equations

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In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example...

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Nonlinear system

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in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved...

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System of polynomial equations

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A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials...

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System of differential equations

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a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear. Also, such a system can...

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Consistent and inconsistent equations

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unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity...

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Diophantine equation

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problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic...

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Ordinary differential equation

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Examples of differential equations Laplace transform applied to differential equations List of dynamical systems and differential equations topics Matrix...

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Equation

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two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true...

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Lagrangian mechanics

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time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Suppose there...

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Overdetermined system

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mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[citation needed] An overdetermined system is almost...

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List of dynamical systems and differential equations topics

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list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations. Deterministic...

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Equations of motion

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In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically...

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System of bilinear equations

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In mathematics, a system of bilinear equations is a special sort of system of polynomial equations, where each equation equates a bilinear form with a...

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Underdetermined system

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mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns...

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Hyperbolic partial differential equation

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characteristics of the equation. This feature qualitatively distinguishes hyperbolic equations from elliptic partial differential equations and parabolic...

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Systems thinking

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dynamical systems continues to this day. In brief, Newton's equations (a system of equations) have methods for their solution. By 1824 the Carnot cycle...

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Algebra

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appear in several linear equations, so-called systems of linear equations. It tries to discover the values that solve all equations at the same time. Abstract...

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Kolmogorov equations

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In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov...

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Hamiltonian mechanics

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Hamilton's equations consist of 2n first-order differential equations, while Lagrange's equations consist of n second-order equations. Hamilton's equations usually...

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Primitive equations

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The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most...

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Coefficient matrix

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consisting of the coefficients of the variables in a set of linear equations. The matrix is used in solving systems of linear equations. In general, a system with...

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Theory of equations

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In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial...

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Differential equation

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Abstract differential equation System of differential equations Dennis G. Zill (15 March 2012). A First Course in Differential Equations with Modeling Applications...

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