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equation Definition

equa·tion (ē kwā′z̸hən, i-)

noun

  1. the act of equating; equalization
  2. the state of being equated; equality, equivalence, or balance; also, identification or association
    1. a complex whole the human equation
    2. an element in a complex whole
  4. a statement of equality between two quantities, as shown by the equal sign (=) a quadratic equation
  5. an expression in which symbols and formulas are used to represent a balanced chemical reaction (Ex.: HSO + 2NaCl = 2HCl + NaSO)

Etymology: ME equacioun < L aequatio

equation Related Forms

equa′·tional adjective

equation Synonyms

equation

n.

equating, comparison, equalization, mathematical statement, formal statement of equivalence; see also comparison 1, 2.

Kinds of equations include: linear, quadratic, conic, cubic.

equation Usage Examples

Converse of object

  • solve: Solving the master equation is the principal purpose of the program.
  • derive: Solution method: The matrix elements of the Hamiltonian are set up one by one according to the equations derived from the theory.
  • rearrange: For direct solution, it must be possible to rearrange the equations so that a formula can be written for every unknown.
  • govern: At the basis of solution of such equations is a discretisation of the governing equations on a given mesh.

Adjective modifier

  • differential: Stochastic differential equations driven by a Wiener process are studied.
  • quadratic: He solved problems such as pairs of simultaneous quadratic equations.
  • partial: Thus, in total there are six partial differential equations to be solved.
  • linear: Von Koch's first results were on infinitely many linear equations in infinitely many unknowns.
  • nonlinear: For most of the nonlinear partial differential equations which we have tested, the running time is no more than 10 seconds.
  • simultaneous: I asked him one day what was the value of the simultaneous equations he was trying to teach us how to solve.

Modifies a noun

  • solver: The algorithms require nonsmooth equation solver as a part.
  • modeling: The use of structural equation modeling in stuttering research: Concepts and directions.

Noun used with modifier

  • differential: Thus, in total there are six partial differential equations to be solved.
  • regression: Using this second regression equation, predict how much money you would have been expected to spend on gambling when you were 14.
  • diffusion: In electromagnetic terms this can be explained using the diffusion equation.
  • reaction-diffusion: No medical knowledge is needed but some familiarity with reaction-diffusion equations would be useful.
  • second-order: Second-order equations: wave, diffusion, Laplace equations; traveling waves, d'Alembert solution, 1-D infinite and semi- infinite regions.
  • first-order: Students are only required to have some training in basic calculus and some familiarity with first-order difference equations.

Preposition: of

motion: Restrictions: The coupled system of equations of motion is integrated under the assumption of axial symmetry.

Preposition: with

coefficient: Given an equation with rational coefficients, how can we determine whether or not it has any rational solutions?