about equations in mathematics the chemistry term chemical equation Image First Equation Ever.png thumb ... of Witte by Robert Recorde 1557 . An equation is a mathematics mathematical Proposition ... . ref cite web url http dictionary.reference.com browse equation title Equation work Dictionary.com ..., a , b , c , d , . The process of expressing the unknowns in terms of the knowns is called Equation solving solving the equation . In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation. In a set simultaneous equations ... and quantities involved. Important types include An algebraic equation is an equation involving ... . A linear equation is an algebraic equation of degree one. A Polynomial Polynomial equations polynomial equation is an equation in which a polynomial is set equal to another polynomial. A transcendental equation is an equation involving a transcendental function of one of its variables. A functional equation is an equation in which the unknowns are Function mathematics functions rather than simple quantities. A differential equation is an equation involving derivative s. An integral equation is an equation involving integral s. A Diophantine equation is an equation where the unknowns are required to be integer s. A quadratic equation Identities One use of equations is in mathematical identity ..., they can be equation solving solved to find the values that satisfy the equality. For example, consider the following. math x 2 x 0 ,. math The equation is true only for two values of x , the solutions of the equation. In this case, the solutions are math x 0 math and math x 1 math . Many mathematicians ref name Nahin reserve the term equation exclusively for the second type, to signify an equality ..., math x 1 2 x 2 2x 1 , math is an identity, while math x 1 2 2x 2 x 1 , math is an equation with solutions math x 0 math and math x 1 math . Whether a statement is meant to be an identity or an equation ... more details
Infobox Television episode Title The Equation Series Fringe TV series Fringe Image Caption Season 1 Episode 8 Airdate November 18, 2008 Production 3T7657 Writer J. R. Orci br David H. Goodman Director Gwyneth Horder Payton Guests William Sadler actor William Sadler as Dr. Bruce Sumner Randall Duk Kim as Dashiell Kim Gillian Jacobs as Joanne Ostler Charlie Tahan as Ben Stockton Adam Grupper as Andrew Stockton Chance Kelly as Mitchell Loeb Kate Hodge as Abby Stockton Michael Cerveris as the List of Fringe ... of Fringe episodes List of Fringe episodes Prev In Which We Meet Mr. Jones Next The Dreamscape The Equation ... of some sort working on an unfinished equation. To discover the child s whereabouts, Olivia ... matter. Production The Equation was written by supervising producer J. R. Orci and co executive producer ... fearnetreview However, Wax continued that The Equation seemed rather pedestrian because nothing ... s Travis Fickett rated The Equation 7.5 10, called it a solid episode despite a few perceived plotholes ... web url http tv.ign.com articles 931 931841p1.html title Fringe The Equation Review first Travis last ... the equation title Fringe The Equation first Jane last Boursaw publisher AOL TV date 2008 11 19 accessdate ... . ref name cinemablend cite web url http www.cinemablend.com television TV Recap Fringe The Equation 13514.html title TV Recap Fringe The Equation first Erin last Dougherty publisher Cinema Blend ... articles the equation,13370 title The Equation first Noel last Murray publisher A.V. Club date 2008 ... a bit hard to swallow . ref cite web url http www.ugo.com tv fringe 108 the equation review title Fringe 1.08 The Equation Review first last publisher UGO Networks date 2008 11 19 accessdate 2011 05 26 ref References reflist 2 External links Wikiquote Fringe The Equation .5B1.08.5D The Equation http www.fox.com fringe recaps season 1 episode 8 The Equation at Fox Broadcasting Company Fox IMDb episode 1248548 Tv.com episode 1236569 Fringe Fringe episodes DEFAULTSORT Equation, The Category Fringe ... more details
Bernoulli equation may refer to Bernoulli differential equation Bernoulli s equation , in fluid dynamics. Euler Bernoulli beam equation , in solid mechanics disambig zh ... more details
Characteristic equation may refer to Characteristic equation calculus , used to solve linear differential equations Characteristic equation, a Characteristic polynomial Characteristic equation characteristic polynomial equation in linear algebra used to find eigenvalues of a matrix Characteristic equation, a polynomial used to solve a recurrence relation Theorem recurrence relation mathdab ... more details
Equation editor may refer to Formula editor Read this for the comparison chart for major mathematical equation editors Microsoft Equation Editor MathType MathMagic equation editor Category Formula editors dab A long comment added to the page to prevent it being listed on Special Shortpages. Generated via Template Longcomment. ... more details
In mathematics , a summation equation or discrete integral equation is an equation in which an unknown function mathematics function appears under a summation sign. The theories of summation equations and integral equation s can be unified as integral equations on time scales ref http web.maths.unsw.edu.au cct tis tomasia IJDE rev.pdf Volterra integral equations on time scales Basic qualitative and quantitative results with applications to initial value problems on unbounded domains , Tomasia Kulik, Christopher C. Tisdell, September 3, 2007 ref using time scale calculus . A summation equation compares to a difference equation as an integral equation compares to a differential equation . The Volterra summation equation is math x t f t sum i m n k t, s, x s math where x is the unknown function, and s, a, t are integers, and f, k are known functions. References references http scholar.google.com scholar?q 22discrete integral equations 22 OR 22summation equations 22 OR 22discrete integral equation 22 OR 22summation equation 22 Summation equations or discrete integral equations Category Integral equations ... more details
In mathematics, the term exact equation can refer either of the following Exact differential equation Closed and exact differential forms Exact differential form disambig ... more details
HH equation may refer to Henderson Hasselbach equation Hodgkin Huxley model disambig Long comment to avoid being listed on short pages ... more details
Stokes equation may refer to the Airy equation the equations of Stokes flow , a linearised form of the Navier Stokes equations in the limit of small Reynolds number Stokes law disambiguation ... more details
An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. See also Linear algebra Indeterminate system Independent variable References Unreferenced date June 2008 Category Linear algebra Linear algebra stub ... more details
Refimprove date January 2010 In mathematics , an algebraic equation , also called polynomial equation over a given Field mathematics field is an equation of the form math P Q math where P and Q are possibly ... 2 frac x 3 3 xy 2 y 2 frac 1 7 math is an algebraic equation over the rationals. Two equations are equivalent if they have the same set of Equation solutions . In particular the equation math P Q math ... to the study of polynomials. An algebraic equation over the rationals can always be converted to an equivalent ... 3 7 and grouping its terms in the first member, the algebraic equation above becomes the algebraic equation math 42y 4 21xy 14x 3 42xy 2 42y 2 6 0 math Although the equation math e T x 2 frac 1 T xy sin T z 2 0 math is not an algebraic equation in four variables x , y , z and T over the rational numbers because sine , exponentiation and 1 T are not polynomial functions . It is an algebraic equation ... T 3 3 frac T 5 5 frac T 7 7 cdots math 1 T and 2 are all elements of Q T . As for any equation, the solutions of an equation are the values of the variables for which the equation is true, but for algebraic ... of the algebraic equation P 0 are the roots of the polynomial P . When solving an equation, it is important to specify in which Set mathematics set the solutions are allowed. For example, for an equation .... In this case the equation is a diophantine equation . One may also look for solutions in the field of complex numbers the fundamental theorem of algebra asserts that a non constant equation has always ... has found the solution of the Cubic function equation of degree 3 and Lodovico Ferrari has solved the Quartic function equation of degree 4 . Finally Niels Henrik Abel has proved in 1824 that the quintic equationequation of degree 5 and the equations of higher degree are not always solvable using radicals. Galois theory , named after variste Galois , were introduced to give criteria deciding if an equation is solvable using radicals. References MathWorld title Algebraic Equation urlname AlgebraicEquation ... more details
Unreferenced date December 2009 In mathematics , LHS is informal shorthand for the left hand side of an equation . Similarly, RHS is the right hand side . Each is solely a name for a term as part of an expression and they are in practice interchangeable, since equality mathematics equality is equivalence relation symmetric . This abbreviation is seldom if ever used in print it is very informal. More generally, these terms may apply to an inequation or inequality mathematics inequality . In the inequality case , there is no symmetry. The right hand side is everything on the right side of a test operator in an Expression mathematics expression . Conversely, the left hand side is everything on the left side. Some examples The expression on the right side right part of the sign is the right side of the equation and the left of the is the left side left part of equation. br br Take x 5 y 8 where x 5 would be the left hand side and y 8 would be the right hand side Homogeneous and inhomogeneous equations In solving mathematical equations, particularly linear simultaneous equations , differential equation s and integral equation s, the terminology homogeneous is often used for equations with the RHS set equal to zero. The corresponding inhomogeneous or nonhomogeneous equation then has the RHS ... operator L , with the difference being that between the equation Lf 0, to be solved for a function f , and the equation Lf g , with g a fixed function, to solve again for f . The point of the terminology appears for L a linear operator . Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution. For example in mathematical physics , the homogeneous equation may correspond to a physical theory formulated in empty space , while the inhomogeneous equation asks for more realistic solutions with some matter, or charged ..., though. See also equal sign DEFAULTSORT Sides Of An Equation Category Mathematical terminology es ... more details
An adjoint equation is a linear differential equation , usually derived from its primal equation using integration by parts . Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization , fluid flow control and uncertainty quantification . References reflist cite journal last Jameson first Antony title Aerodynamic Design via Control Theory journal Journal of Scientific Computing volume 3 issue 3 year 1988 DEFAULTSORT Adjoint Equation Category Differential calculus Applied math stub Math stub Engineering stub Mech engineering stub ru ... more details
In mathematics , more specifically in the study of dynamical system s and differential equation s, a Li nard equation ref Li nard, A. 1928 Etude des oscillations entretenues, Revue g n rale de l lectricit 23 , pp. 901 912 and 946 954. ref is a second order differential equation, named after the French physicist Alfred Marie Li nard . During the development of radio and vacuum tube technology, Li nard equations were intensely studied as they can be used to model oscillating circuit s. Under certain additional assumptions Li nard s theorem guarantees the uniqueness and existence of a limit cycle for such a system. Definition Let f and g be two continuously differentiable functions on R , with g an odd function and f an even function then the second order ordinary differential equation of the form math d 2x over dt 2 f x dx over dt g x 0 math is called the Li nard equation . Li nard system The equation can be transformed into an equivalent two dimensional system of ordinary differential equation s. We define math F x int 0 x f xi d xi math math x 1 x , math math x 2 dx over dt F x math then math begin bmatrix dot x 1 dot x 2 end bmatrix mathbf h x 1, x 2 begin bmatrix x 2 F x 1 g x 1 end bmatrix math is called a Li nard system . Alternatively, since Li nard equation itself also belongs to autonomous differential equation , the substitution math v dx over dt math leads the Li nard equation to a first order differential equation math v dv over dx f x v g x 0 math which belongs to Abel equation of the second kind . ref http eqworld.ipmnet.ru en solutions ode ode0317.pdf Li nard equation at eqworld . ref ref http eqworld.ipmnet.ru en solutions ode ode0125.pdf Abel equation of the second ... dt x 0 math is a Li nard equation. Li nard s theorem A Li nard system has a unique and Stability ... also Autonomous differential equation Abel equation of the second kind Footnotes reflist External links PlanetMath title LienardSystem urlname LienardSystem DEFAULTSORT Lienard equation Category Dynamical ... more details
In geometry , the Ces ro equation of a plane curve is an equation relating curvature math kappa math to arc length math s math . It may also be given as an equation relating the Radius of curvature mathematics radius of curvature math R math to arc length . These are equivalent because math R 1 kappa math . Two congruence geometry congruent curves will have the same Ces ro equation. It is named after Ernesto Ces ro . Some curves have a particularly simple representation by a Ces ro equation. Some examples are line geometry Line math kappa 0 math . Circle math kappa 1 alpha math , where math alpha math is the radius. Logarithmic spiral math kappa C s math , where math C math is a constant. Involute Circle involute math kappa C sqrt s math , where math C math is a constant. Cornu spiral math kappa Cs math , where math C math is a constant. Catenary math kappa frac a s 2 a 2 math . The Ces ro equation of a curve is related to its Whewell equation in the following way, if the Whewell equation is math varphi f s math then the Ces ro equation is math kappa f s math . References cite book title The Mathematics Teacher year 1908 publisher National Council of Teachers of Mathematics pages 402 cite book author Edward Kasner title The Present Problems of Geometry publisher Congress of Arts and Science Universal Exposition, St. Louis year 1904 pages 574 cite book author J. Dennis Lawrence title A catalog of special plane curves publisher Dover Publications year 1972 isbn 0 486 60288 5 pages 1 5 External links MathWorld title Ces ro Equation urlname CesaroEquation MathWorld title Natural Equation urlname NaturalEquation http www.2dcurves.com derived curvature.html curvature Curvature Curves at 2dcurves.com. Category Curves eo Ekvacio de Ces ro sl Ces rojeva ena ba ... more details
The Abel equation , named after Niels Henrik Abel , is special case of functional equation s which can be written in the form math f h x h x 1 , math or math alpha f x alpha x 1 math and shows non trivial properties at the iteration. Equivalence These equations are equivalent. Assuming that is an invertible function , the second equation can be written as math alpha 1 alpha f x alpha 1 alpha x 1 , . math Taking math x alpha 1 y math , the equation can be written as math f alpha 1 y alpha 1 y 1 , . math For a function f x assumed to be known, the task is to solve the functional equation for the function sup 1 sup , possibly satisfying additional requirements, such as sup 1 sup 0 1. The change of variables s sup x sup x , for a real parameter s , brings Abel s equation into the celebrated Schr der s equation , f x s x . History Initially, the equation in the more general form ref name abel cite journal url http gdz.sub.uni goettingen.de ru dms load img ?PPN PPN243919689 0001&DMDID dmdlog6 author Abel, N.H. coauthors title Untersuchung der Functionen zweier unabh ngig ver nderlichen Gr en x und y, wie f x, y , welche die Eigenschaft haben, ... journal Journal f r die reine und angewandte Mathematik volume 1 pages 11 15 year 1826 ref ref name s cite journal url http projecteuclid.org ... in the case of single variable, the equation is not trivial, and requires special analysis ref ... Jitka Laitochov title Group iteration for Abel s functional equation abstract Studied is the Abel functional equation f x x 1 ref In the case of linear transfer function, the solution can be expressed ... author G. Belitskii coauthor Yu. Lubish title The Abel equation and total solvability of linear ... Equation of tetration is special case of Abel s equation, with math f exp math . In the case of integer argument, the equation is just a recurrent procedure. See also Functional equation Abel function Schr der s equation References references Category Niels Henrik Abel Category Functional equations ... more details
. Dispersionless Hirota equation See also Integrable systems Nonlinear Schr dinger equation Nonlinear systems Davey Stewartson equation Dispersive partial differential equation Kadomtsev Petviashvili equation Korteweg de Vries equation References Kodam Y., Gibbons J. Integrability of the dispersionless ... representation and dispersionless DS equation , ArXiv 0709.4148 Konopelchenko B.G., Moro A. Integrable ... more details
In mathematics , Chaplygin s equation , named after Sergei Alekseevich Chaplygin , is a partial differential equation useful in the study of transonic fluid mechanics flow . ref cite book last1 Landau first1 L. D. authorlink1 Lev Landau last2 Lifshitz first2 E. M. authorlink2 Evgeny Lifshitz title Fluid Mechanics edition 2 year 1982 publisher Pergamon Press page 432 ref It is math Psi theta theta frac v 2 1 frac v 2 c 2 Psi vv v Psi v 0. math Here, math c c v math is the speed of sound , determined by the equation of state of the fluid and Bernoulli s principle . References Reflist DEFAULTSORT Chaplygin s Equation Category Partial differential equations Category Equations fi T aplyginin yht l ... more details
An indeterminate equation , in mathematics , is an equation for which there is an infinite set of solutions for example, 2x y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information. For example, the equations math ax by c math math x 2 Py 2 1 math where a, b, c, and P are given integers provided that P is not a square number , are indeterminate equations. Equations of the second form are named Pell s equation s. See also Indeterminate system Indeterminate variable Linear algebra References Unreferenced date August 2008 Category Algebra algebra stub es Ecuaci n indeterminada ko nl Onbepaalde vergelijking nn Ubestemt uttrykk uk ... more details
In the mathematics mathematical theory of partial differential equations , a Monge equation , named after Gaspard Monge , is a first order partial differential equation for an unknown function u in the independent variables x sub 1 sub ,..., x sub n sub math F left u,x 1,x 2, dots,x n, frac partial u partial x 1 , dots, frac partial u partial x n right 0 math that is a polynomial in the partial derivatives of u . Any Monge equation has a Monge cone . Classically, putting u x sub 0 sub , a Monge equation of degree k is written in the form math sum i 0 cdots i n k P i 0 dots i n x 0,x 1, dots,x k , dx 0 i 0 , dx 1 i 1 cdots dx n i n 0 math and expresses a relation between the differential of a function differentials dx sub k sub . The Monge cone at a given point x sub 0 sub , ..., x sub n sub is the zero locus of the equation in the tangent space at the point. The Monge equation is unrelated to the second order Monge Amp re equation . Category Partial differential equations mathanalysis stub ... more details
Noref date November 2009 The Prony equation named after Gaspard de Prony is a historically important equation in hydraulics , used to calculate the head loss due to friction within a given run of pipe. It is an empirical equation developed by France Frenchman Gaspard de Prony in the 19th century math h f frac L D aV bV 2 math where h sub f sub is the head loss due to friction, calculated from the ratio of the length to diameter of the pipe L D , the velocity of the flow V , and two empirical factors a and b to account for friction. This equation has been supplanted in modern hydraulics by the Darcy Weisbach equation , which used it as a starting point. Category Equations of fluid dynamics mathapplied stub ca Equaci de Prony es Ecuaci n de Prony fr quation de Prony pt Equa o de Prony ru sl Pronyjeva ena ba uk ... more details
Orphan date July 2011 The Rodrigues equation is an equation used in chromatography to describe the efficiency of a bed of permeable large pore particles. It is thus an extension of Van Deemter s equation . It was developed by Alirio E. Rodrigues et al. . ref name Rodrigues1997 cite journal title Permeable packings and perfusion chromatography in protein separation journal Journal of Chromatography B author Alirio E. Rodrigues volume 699 issue 1 2 date 10 October 1997 pages 47 61 doi 10.1016 S0378 4347 97 00197 7 ref Equation The equation is math HETP A frac B u C cdot f lambda cdot u math Where HETP is the height equivalent to a theoretical plate A Eddy diffusion B Longitudinal diffusion C Resistance to mass transfer u Flow rate math f lambda frac 3 lambda left frac 1 tanh lambda frac 1 lambda right math math lambda math Intraparticular P clet number References reflist Category Chromatography Category Equations analytical chem stub ... more details
In a physical and especially geophysical simulation context, a diagnostic equation or diagnostic model is an equation or model that links the values of these variables simultaneously, either because the equation or model is time independent, or because the variables all refer to the values they have at the same identical time. This is by opposition to a prognostic equation . For instance, the so called ideal gas law PV nRT of classical thermodynamics relates the state variable s of that gas, all estimated at the same time. It is understood that the values of any one of these variables can change in time, but the relation between these variables will remain valid at each and every particular instant, which implies that one variable cannot change its value without the value of another variable also being affected. References James R. Holton 2004 An Introduction to Dynamic Meteorology , Academic Press, International Geophysics Series Volume 88, Fourth Edition, 535 p., ISBN 0123540151, ISBN 978 0123540157. External links http amsglossary.allenpress.com glossary search?id diagnostic equation1 Amsglossary.allenpress.com DEFAULTSORT Diagnostic Equation Category Atmospheric dynamics no Diagnostisk ligning nn Diagnostisk likning ... more details
In mathematics, the replicator equation is a deterministic monotone non linear and non innovative game dynamic used in evolutionary game theory . The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness landscape ... type constant. This important property allows the replicator equation to capture the essence of selection . Unlike the quasispecies equation, the replicator equation does not incorporate mutation ... form is given by the differential equation math dot x i x i f i x phi x , quad phi x sum i 1 n ..., the equation is defined on the n dimensional simplex . The replicator equation assumes a uniform population ... equations, such as the quasispecies equation. In application, populations are generally finite, making ... upon the population distribution, which allows the replicator equation to be written in the form ... to be stochastic. Since the replicator equation is non linear, an exact solution is difficult to obtain even in simple versions of the continuous form so the equation is usually analyzed in terms of stability. The replicator equation in its continuous and discrete forms satisfies the Folk theorem ... of the equation. The solution of the equation is often given by the set of evolutionarily stable state ... equation once a strategy becomes extinct there is no way to revive it. Phase portrait solutions for the continuous linear fitness replicator equation have been classified in the two and three dimensional ... portraits increases rapidly. Relationships to other equations The continuous replicator equation on math n math types is equivalent to the Generalized Lotka&ndash Volterra equation in math n 1 math dimensions ... Volterra variable. The continuous replicator dynamic is also equivalent to the Price equation see ... equation which incorporates mutation is given by the replicator mutator equation, which ... j math to type math i math . This equation is a simultaneous generalization of the replicator equation ... more details
Encyclopedia
top
