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Longman Dictionary of Contemporary English
mathematical equation/calculation/formula etc
quadratic equation
solve an equation
▪ At the age of six, he could solve complicated mathematical equations.
▪ These are second order differential equations for the four metric functions.
▪ Some of the math is quite sophisticated, using differential equations, linear algebra, and covariance matrices.
▪ Typically, such a plant's behaviour can be described by a differential equation which depends on coefficients.
▪ The mathematical models of the glycolytic pathway take the form of ordinary nonlinear differential equations.
▪ Goffman's curves fitted very well to those derived by differential equations validated in epidemiology.
▪ In fact, the information-processing mechanisms are designed for implementing the systems of differential equations associated with neural networks.
▪ These are usually formulated in terms of differential equations. 2.
▪ I progressed happily through differential equations and linear algebra to upper-level engineering courses on time-series analysis and computer programming.
▪ The following equation forms the basis of the kinetic theory of gases.
▪ The cross-sectional test took the form of the following equation:.
▪ For the association-dissociation reactions, these relationships may be written as linear equations for the observed parameters or their powers.
▪ In this limit the Einstein equation reduces to a linear wave equation.
▪ We then obtain n - 2 linear algebraic equations for the n - 2 unknowns pi.
▪ After such studies, concentration profiles of the solutes are obtained as the solutions of the linear mass transfer equations.
▪ Chapter 6 deals in general terms with the solution of sets of linear differential equations with constant coefficients.
▪ Solving all the necessary mathematical equations on paper is next to impossible.
▪ That world evolves in a clear and deterministic way, being governed by precisely formulated mathematical equations.
▪ Cowan set up a mathematical equation that represented the neural activity, and built lateral inhibition into it.
▪ He often walks through entire discussions performing mathematical equations without the aid of a calculator.
▪ You can use this function to accept and evaluate an expression, such as a mathematical equation, whilst the program is running.
▪ Another use would be in a graph plotting program to accept the mathematical equation you wished to plot.
▪ In arguing for pointillism, he quoted the scientific treatises consulted by Seurat and even printed mathematical equations.
▪ His mind reeling with the difficult mathematical equations, he suddenly heard a soft knocking at the door.
▪ One boy was solving a quadratic equation, another was engaged with Euclid.
▪ And so I am pasted to this leaning morass, observing the simplest of equations.
▪ The simplest Cartesian equation is y ² 4 ax.
▪ These models are presented as examples of what can be done with simple equations.
▪ I couldn't rearrange a simple equation.
▪ The field equations for colliding electromagnetic waves have already been obtained in Chapter 6.
▪ Their approach commences by rewriting the field equations in the form of Ernst's equation as described in Chapter 11.
▪ The question of when solutions of the Lorenz equations are periodic and when non-periodic is in fact a matter of some complexity.
▪ Variables were entered into or removed from the logistic regression equation one at a time.
▪ Daily total caloric requirements were calculated from Long's equation modified for ideal body weight.
▪ The latter can now be calculated from the Boltzmann equation.
▪ Typically, such a plant's behaviour can be described by a differential equation which depends on coefficients.
▪ Loyalty schemes apparently do not enter the equation.
▪ With the particular choice of co, p4 enters into the last equation only.
▪ Performance elements do enter into the equation.
▪ But other factors enter into the equation.
▪ The question of whether we want the food or not doesn't enter into the equation.
▪ Ideology does not enter the equation, and never has.
▪ In the real world, money can't help but enter the equation.
▪ Nowhere does quality of product or job satisfaction enter the accountants' equations of profit and loss.
▪ The Euler equation is given below.
▪ A second property is that the local distances are given by a metric equation in the Gaussian coordinate separations.
▪ From the production and factor supply equations, we obtain the basic growth equation.
▪ As angles are passed that satisfy the Bragg equation, signals flash out.
▪ Given that an equilibrium exists, it can be found by solving these equations.
▪ Using the equilibrium condition Q, Qi solve the equations to determine equilibrium price.
▪ First, we can not solve the equations for the very large number of particles involved.
▪ One boy was solving a quadratic equation, another was engaged with Euclid.
▪ First, we can not solve the equations.
▪ We next go on to solve these equations of motion.
▪ But it is just too hard to solve the equations when there are more than a few particles involved.
▪ Even in the simpler Newtonian theory of gravity, one can solve the equations exactly only in the case of two particles.
▪ Explanatory sketches, diagrams, and photographs substitute for equations and help make up for lack of prior knowledge of other sciences.
▪ The flow-of-funds equation All these effects on money supply can be summarized using a flow-of-funds equation.
▪ Some of the math is quite sophisticated, using differential equations, linear algebra, and covariance matrices.
▪ We can use the Arrhenius equation to look at the effect of the temperature and activation energy on reaction rate.
▪ As in the algebra example above, the supply and demand curves can be approximated using equations for straight lines.
▪ For the association-dissociation reactions, these relationships may be written as linear equations for the observed parameters or their powers.
▪ He wrote the second equation on the blackboard.
▪ Could one write an equation: one association one synapse?
▪ I tried sketching network diagrams, writing input equations, summation equations, and transfer equations.
▪ We are particularly interested in the comparative statics, and for this purpose we write down the equations of change.
▪ Miss Pinkerton, the math teacher; writes problems and equations on the board, and I listen intently to her explanations.
▪ The standard molar enthalpy of formation could have two different values depending on how we write the equation.
▪ You could write an equation for a process that you could actually solve.
▪ If you're trying to get healthy by losing weight, exercise should be part of the equation.
▪ A daring proposal was made to reconcile the continuity of the Schrödinger equation with the discontinuity of empirical experience.
▪ From the production and factor supply equations, we obtain the basic growth equation.
▪ Mathematicians scribble equations on blackboards and program supercomputers to make the billions of calculations needed to break a tough code.
▪ My equations were visual and phonetic.
▪ Some of the math is quite sophisticated, using differential equations, linear algebra, and covariance matrices.
▪ The equations preceded the actual observations.
▪ The restrictions generated by rational expectations models are very often non-linear and are also imposed across equations rather than in a single equation.
▪ What A Present View forces us to do is to reconsider a traditional equation between humanism and liberalism.
The Collaborative International Dictionary

Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F.

  1. A making equal; equal division; equality; equilibrium.

    Again the golden day resumed its right, And ruled in just equation with the night.

  2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.

  3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion.

    Absolute equation. See under Absolute.

    Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time.

    Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse.

    Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities.

    Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve.

    Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox.

    Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times.

    Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round.

    Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time.

    Normal equation. See under Normal.

    Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals.

    Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity.

Douglas Harper's Etymology Dictionary

late 14c., a term in astrology (from French équation, 14c.); general sense of "action of making equal" is from 1650s, from Latin aequationem (nominative aequatio) "an equal distribution, a sharing in common," noun of state from past participle stem of aequare (see equal (adj.)). Mathematical sense is from 1560s, on notion of equalizing the expressions; Chemistry sense is from 1807.


n. 1 (senseid en assertion)(context mathematics English) An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity. 2 (context astronomy English) A small correction to observed values to remove the effects of systematic errors in an observation.

  1. n. a mathematical statement that two expressions are equal

  2. a state of being essentially equal or equivalent; equally balanced; "on a par with the best" [syn: equality, equivalence, par]

  3. the act of regarding as equal [syn: equating]


In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. Variables are also called unknowns and the values which satisfy the equality are called solutions of the equation. There are two kinds of equations: identity equations and conditional equations. An identity equation is true for all values of the variable. An conditional equation is true for only particular values of the variables.

Each side of an equation is called a member of the equation. Each member will contain one or more terms. The equation,

Ax + Bx + C = y

has two members: Ax + Bx + C and y. The left member has three terms and the right member one term. The variables are x and y and the parameters are A, B, and C.

An equation is analogous to a scale into which weights are placed. When equal weights of something (grain for example) are place into the two pans, the two weights cause the scale to be in balance and are said to be equal. If a quantity of grain is removed from one pan of the balance, an equal amount of grain must be removed from the other pan to keep the scale in balance. Likewise, to keep an equation in balance, the same operations of addition, subtraction, multiplication and division must be performed on both sides of an equation for it to remain an equality.

In geometry, equations are used to describe geometric figures. As equations that are considered, such as implicit equations or parametric equations have infinitely many solutions, the objective is now different: instead of given the solutions explicitly or counting them, which is impossible, one uses equations for studying properties of figures. This is the starting idea of algebraic geometry, an important area of mathematics.

Algebra studies two main families of equations: polynomial equations and, among them the special case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial. Linear equations have the form ax + b = 0, where a and b are parameters. To solve equations from either family, one uses algorithmic or geometric techniques, that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.

Differential equations are equations that involve one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model processes that involve the rates of change of the variable, and are used in areas such as physics, chemistry, biology, and economics.

The " =" symbol, which appears in every equation, was invented in 1557 by Robert Recorde, who considered that nothing could be more equal than parallel straight lines with the same length.

Equation (band)

Equation were a young Devon-based folk band formed in 1995 to combine the core talents of the Lakeman Brothers with Kathryn Roberts and Kate Rusby, later replaced for a spell by Cara Dillon. The band remains an unsung supergroup of the contemporary British folk rock scene of the 1990s as its members went on to become award winning recording artists in their own right.

Their first single He loves me was originally released in 1996 on the Blanco Y Negro-WEA label and was followed by four studio albums.

The Times newspaper reviewed their first official album release Hazy Daze in 1998, scoring 7/10 and giving a favourable comparison to Fairport Convention.

Equation (disambiguation)

An equation in mathematics is a formula stating that two expressions have the same value.

Equation may also refer to:

  • Chemical equation, a symbolic representation of a chemical reaction
  • Equation of time, the difference between solar time, as shown by a sundial, and mean time, as shown by a clock that runs at constant speed
  • Equation clock, a clock that contains a mechanism that embodies the equation of time, so the clock shows solar time
  • Equation of state, a relationship between physical conditions and the state of a material
  • Equation (band), an English folk band formed in 1996
  • Equation Group, a computer espionage group

Usage examples of "equation".

I needed to close that chapter on my life and take Adeem out of the equation forever.

Joe was the smart one, the one who could calculate algebraic equations in his head, the one who would go on to a brilliant career in finance, just like his father.

Queen Victoria had ever called an urgent meeting of her counsellors, and ordered them to invent the equivalent of radio and television, it is unlikely that any of them would have imagined the path to lead through the experiments of Ampere, Biot, Oersted and Faraday, four equations of vector calculus, and the judgement to preserve the displacement current in a vacuum.

He flipped over to another screen and was doodling equations when the door opened and Tchar and the ardass entered.

It was all very much like being faced by an algebraic problem containing many unknown quantities and having only one biquadratic equation with which to solve it.

The solution of cubic and of biquadratic equations, at first only in certain particular forms, but later in all forms, was mastered by Tartaglia and Cardan.

Ray Chen, for example, had been a go-to man for gauge boson and multidimensional field equations but even he bowed his head a few times and consulted with a pure mathematician in Britain.

She passed a board that was covered with quantum equations, another, half-erased already, that held only two clean and concise Bussard drive efficiency calculations, the kind Li had wrestled with in her OCS math courses.

McCoy, your homiletics point out initial concauses, yet you fail to see that no one element can stand alone in a progressive equation.

Or putting it another way, the equations expressing all physical laws should be covariant between inertial frames.

He had a guiding principle: nature seemed to like equations stated in covariant differential forms.

I checked with Coypu and he says it is possible and he is muttering over the equations now.

Injected at the speed of light, but in a digitized and orderly manner, matter broken down into energy might well be reduced to an equation, or series of equations, written in energy itself.

I was studying the eigenvalue spectrum of the Taylor-Goldstein equation, trying to develop a new methodology for examining the stability of a particular class of fluid flows.

The solution results in eigenvalues of zero on both sides of the equation.