An equation, in a mathematical context, is generally understood to mean a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example
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Some articles on equation:
... If an equation in algebra is known to be true, the following operations may be used to produce another true equation Any real number can be added to both sides ... For example, the equation has 2 sets of solutions (with any x) and (with any y) ... sides to the exponent of 2 (which means, applying the function to both sides of the equation) changes our equation into, which not only has all the previous solutions but also introduces a new set of ...
... where there is no superconducting current and the equation for ψ simplifies to This equation has a trivial solution ψ = 0 ... the superconducting transition temperature, the above equation is expected to have a non-trivial solution (that is ψ ≠ 0) ... Under this assumption the equation above can be rearranged into When the right hand side of this equation is positive, there is a nonzero solution for ψ (remember that ...
... can be used to derive the Brownian motion of a particle from the Langevin equation ... According to that equation, the motion of a particle of mass m with velocity v is governed by Newton's second law where Frnd is a random force representing the random collisions of the particle and ... The dot product of this equation with the position vector r, after averaging, yields the equation for Brownian motion (since the random force Frnd is uncorrelated with the position r) ...
... For a stationary shock, and for the 1D Euler equations we have In view of equation (12) we can simplify equation (14) to which is a statement of ... Substituting and from equations (12) and (13) into equation (15) yields the following relationship where represents specific enthalpy of the fluid ... Eliminating internal energy in equation (15) by use of the equation-of-state, equation ( 4), yields From physical considerations it is clear that both the ...
... In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics ...
More definitions of "equation":
- (noun): A state of being essentially equal or equivalent; equally balanced.
Synonyms: equality, equivalence, par
- (noun): A mathematical statement that two expressions are equal.
Famous quotes containing the word equation:
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)