equation

Definition of equation in English English dictionary: A small correction to observed values to remove the effects of systematic errors in an observation; 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; {n} a bringing of things to an equality; A statement showing the equality of two expressions usually separated by left and right signs and joined by an equals sign; a mathematical statement that says that two expressions have the same value; Two expressions, separated by an equals sign (=) For example y = x + 3 is an equation; {i} making equal; statement demonstrating the equality of two quantities (Mathematics); equally balanced state; In astronomy, a small correction to observed values to remove the effects of systematic errors in an observation; an algebraic statement that has an equal sign; A symbolic statement that can be used to do a calculation For example, x = 12y, where x is the number of inches in y feet; An equation is a mathematical statement saying that two amounts or values are the same, for example 6x4=12x2; the act of regarding as equal a mathematical statement that two expressions are equal; a state of being essentially equal or equivalent; equally balanced; "on a par with the best"; two algebraic expressions that are set equal to each other; the act of regarding as equal; An equation is a situation in which two or more parts have to be considered together so that the whole situation can be understood or explained. The equation is simple: research breeds new products New plans have taken chance out of the equation. see also equate. Statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way. Equations vary in complexity from simple algebraic equations (involving only addition or multiplication) to differential equations, exponential equations (involving exponential expressions), and integral equations. They are used to express many of the laws of physics. See also system of equations. algebraic equation chemical equation continuity equation difference equation differential equation Drake equation Green Bank equation integral equation Laplace's equation motion equation of ordinary differential equation partial differential equation quadratic equation Schrödinger equation state equation of Maxwell's equations system of equations simultaneous equations; 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; A statement that two mathematical expressions are equal, such as: 3x + y = 7; An equation is a math sentence that says that 2 things are equal An equation always has an equal (=) sign The thing or things that are on the left side of the equal sign are equal to the things on the right side of the equal sign Here are a few equations: X = Y + 5 A = B - 4 Z = 3 A C = D (circumference of a circle) A = W H (area of a rectangle with width W and height H) E = M C2 (Einstein's famous equation) In the first equation, if Y is 2, then X must be 2 + 5 or 7 to make the equation true In the second equation, if B is 10, then A must be 6 to make the equation true In the third equation, the number next to the letter means multiply the value of the variable represented by "A" by 3 So if A is 4, then Z must be 12 to make the third equation true Now here's a problem for you: In the first equation, if Y were 10, what would X be?; a mathematical expression containing an equals sign The expression on the left hand side of the equals sign must have the same value as the expression on the right hand side Equations often contain algebra; a statement that shows two expressions having the same value; An equation is a statement of equality between two algebraic expressions with one or more unknowns (See also system of equations ) Linear equation in one unknown: 3x -1 = 5 To solve 3x - 1 = 5 3x = 6 x = 2 (root/solution) Quadratic equation in one unknown: x2 - x - 2 = 0 To find the solution of x2 - x - 2 = 0 (x - 2)(x + 1) = 0 x - 2 = 0 x + 1 = 0 x = 2 x = -1 (solutions) Linear equation in two unknowns: 2x + y = 3; An algebraic expression asserting the equality of two quantities Example: x + 4 = y -10; a mathematical statement that two expressions are equal; a quantity added or subtracted in equating (comparing) a computation; Letters and numbers connected by the = sign c=2 x pi is the equation for the circumference of a circle with a radius of 2 See also formula, expression, function, terms, like terms, substitute and symbol; A mathematical statement using an equals sign, can be very simple e g 5+5 = 10, or more complex 5t + 7q = 23y; This is a mathematical sentence stating that two expressions are equal; A making equal; equal division; equality; equilibrium; 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; A mathematical sentence stating that two expressions are equal; a math statement using "=" as the verb -- "Typically there is a part of the equation that is unknown " (98)
equation division: the second of the two divisions of meiosis, a type of cell division
equation in one unknown: mathematical formula in which there is a need to determine an unknown (i.e. X+1=2)
equation in three unknowns: mathematical formula containing 3 unknown values
equation in two unknowns: mathematical formula containing two unknown values
equation of motion: equation that shows the change of velocity of a material over time
equation of motion: Mathematical formula that describes the motion of a body relative to a given frame of reference, in terms of the position, velocity, or acceleration of the body. In classical mechanics, the basic equation of motion is Newton's second law (see Newton's laws of motion), which relates the force on a body to its mass and acceleration. When the force is described in terms of the time interval over which it is applied, the velocity and position of the body can be derived. Other equations of motion include the position-time equation, the velocity-time equation, and the acceleration-time equation of a moving body
equation of state: Any of a class of equations that relate the pressure P, volume V, and temperature T of a given substance in thermodynamic equilibrium. For example, the equation PV = nRT, where n is the number of moles of gas and R is the universal gas constant, relates the pressure, volume, and temperature of a perfect gas. Real gases, solids, and liquids have more complicated equations of state. See also thermodynamics
Arrhenius equation: An equation which approximates the dependence of the rate of any chemical reaction on the temperature
Diophantine equation: A polynomial equation whose variables are only permitted to assume integer values
Dirac equation: A relativistic wave equation that describes an electron (and similar particles); it predicted the existence of antiparticles
Drake equation: A formula for calculating the probability of civilizations existing elsewhere in the Milky Way galaxy and of their ability to communicate with Earth
Einstein field equation: A symmetric 4 x 4 tensor equation in general relativity in which the gravitational force is described as a curvature of spacetime caused by matter and energy
Kepler's equation: the mathematical relationship between the mean anomaly (M) and the eccentric anomaly (E) of a planet in an elliptical orbit with eccentricity ( \textstyle \epsilon ). M = E - \epsilon \cdot \sin(E)
Navier-Stokes equation: a partial differential equation which describes the conservation of linear momentum for a Newtonian incompressible fluid
Pell's equation: The diophantine equation x^2 - my^2 = 1 for a given integer m., to be solved in integers x and y
Schrödinger's wave equation: A three-dimensional partial differential equation which determines the evolution of a quantum mechanical wave function
algebraic equation: A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3
chemical equation: a symbolic representation of a chemical reaction; reactants are represented on the left, and products on the right
2Na + 2H2O => 2NaOH + H2.
cubic equation: A polynomial equation whose greatest exponent is 3
delay differential equation: a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times
difference equation: An equation involving an ordered sequence or real numbers (\left\{a_n\right\}_{n=1}^\infty) and some number if it's differences, where the first difference is defined as \Delta(a_n) = a_{n+1} - a_n\, and the kth difference is defined recursively as \Delta^k(a_n) = \Delta^{k-1}(a_{n+1}) - \Delta^{k-1}(a_n)\
difference equation: more broadly, any recurrence relation
differential equation: an equation involving the derivatives of a function
exponential equation: A type of equation which includes a variable located in the exponent; for example, e^x = 1\
half-equation: Either of two equations that describe each half of a redox reaction
integral equation: An equation involving a function f(x) and integrals of that function to be solved for f(x)
linear equation: A polynomial equation of the first degree (such as x = 2y - 7)
ordinary differential equation: An equation involving the derivatives of a function of only one independent variable
parametric equation: a set of equations that defines the coordinates of the dependent variables (x, y and z) of a curve or surface in terms of one or more independent variables or parameters
partial differential equation: a differential equation that involves the partial derivatives of a function of several variables
polar equation: An equation defining a curve in terms of radius and angle
polynomial equation: Any algebraic equation in which one or both sides are in the form of a polynomial
quadratic equation: a polynomial equation of the second degree
stochastic differential equation: a type of differential equation in which one or more of the terms is a stochastic process resulting in a solution which is itself a stochastic process
henderson hasselbalch equation: (Kimya) In chemistry, the Henderson–Hasselbalch equation describes the derivation of pH as a measure of acidity (using pKa, the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions (it is widely used to calculate the isoelectric point of proteins)
point-slope equation: y – y1 = m(x – x1), where m is the slope and (x1, y1) is a point on the line. Point-slope is the form used most often when finding the equation of a line
Diophantine equation: An algebraic equation with two or more variables whose coefficients are integers, studied to determine all integral solutions
Drake equation: or Green Bank equation Equation claimed to yield the number of technically advanced civilizations capable of interstellar communication in the Milky Way Galaxy as a function of several factors conducive to evolution of intelligent life with technological capabilities. It was largely developed by Frank D. Drake (b. 1930) in 1961 at a SETI conference in Green Bank, W.Va. Of all the stars that form in the Galaxy, only some will give rise to life-supporting planets, and of those planets, only some will generate life capable of high technology and yet able to avoid technological destruction. Because the numbers for each factor are poorly known, the results generated vary from zero to millions
Laplace's equation: In mathematics, a partial differential equation whose solutions (harmonic functions) are useful in investigating physical problems in three dimensions involving gravitational, electrical, and magnetic fields, and certain types of fluid motion. Named for Pierre-Simon Laplace, the equation states that the sum of the second partial derivatives (the Laplace operator, or Laplacian) of an unknown function is zero. It can apply to functions of two or three variables, and can be written in terms of a differential operator as F = 0, where is the Laplace operator
Schrödinger equation: Fundamental equation developed in 1926 by Erwin Schrödinger that established the mathematics of quantum mechanics. The equation determines the behaviour of the wave function that describes the wavelike properties of a subatomic system. It relates kinetic energy and potential energy to the total energy, and it is solved to find the different energy levels of the system. Schrödinger applied the equation to the hydrogen atom and predicted many of its properties with remarkable accuracy. The equation is used extensively in atomic, nuclear, and solid-state physics. See also wave-particle duality
algebraic equation: Mathematical statement of equality between algebraic expressions. An expression is algebraic if it involves a finite combination of numbers and variables and algebraic operations (addition, subtraction, multiplication, division, raising to a power, and extracting a root). Two important types of such equations are linear equations, in the form y = ax + b, and quadratic equations, in the form y = ax^2 + bx + c. A solution is a numerical value that makes the equation a true statement when substituted for a variable. In some cases it may be found using a formula; in others the equation may be rewritten in simpler form. Algebraic equations are particularly useful for modeling real-life phenomena
biquadratic equation: an equation of the fourth degree
chemical equation: Method of writing the essential features of a chemical reaction using chemical symbols (or other agreed-upon abbreviations). By convention, reactants (present at the start) are on the left, products (present at the end) on the right. A single arrow between them denotes an irreversible reaction, a double arrow a reversible reaction. The law of conservation of matter (see conservation law) requires that every atom on the left appear on the right (the equation must balance); only their arrangements and combinations change. For example, one oxygen molecule combining with two hydrogen molecules to form two water molecules is written 2H2 + O2 2H2O. The dissociation of salt into sodium and chloride ions is written NaCl Na^+ + Cl^-. See also stoichiometry
difference equation: Equation involving differences between successive values of a function of a discrete variable (i.e., one defined for a sequence of values that differ by the same amount, usually 1). A function of such a variable is a rule for assigning values in sequence to it. For example, f(x + 1) = xf(x) is a difference equation. Methods developed for solving such equations have much in common with methods for solving linear differential equations, which difference equations are often used to approximate
differential equation: an equation containing differentials of a function
differential equation: equation that expresses the connection between a variable and its derivative and whose solution is a function (Mathematics)
differential equation: An equation that expresses a relationship between functions and their derivatives. Mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by functions. Differential equations are very common in physics, engineering, and all fields involving quantitative study of change. They are used whenever a rate of change is known but the process giving rise to it is not. The solution of a differential equation is generally a function whose derivatives satisfy the equation. Differential equations are classified into several broad categories. The most important are ordinary differential equations (ODEs), in which change depends on a single variable, and partial differential equations (PDEs), in which change depends on several variables. See also differentiation
equations: Students will be expected to write balanced (their highlighting, not mine) equations and should be encouraged to show state symbols Ionic equations should be used where appropriate (like redox reactions and electrolysis, to name two) The use of [H] and [O] to show reducing and oxidising agents in equations in organic (ie not inorganic or physical) chemistry is acceptable (note that acceptable is not the same as good or excellent or 'the best chemistry I've seen since Bobby Boyle started messing around with gases')
equations: plural of equation
equations: a statement that two expressions are equal
exponential equation: an equation involving exponential functions of a variable
integral equation: In mathematics, an equation with an unknown function within an integral. An example is
linear equation: Linear equation in one variable can be written in the form ax = b, a 0 A linear equation in two variables can be written in the form ax + by = c
linear equation: An equation whereby letters represent real numbers and whose graph is a line
linear equation: This is an equation, such as y = x + 2, which produces a graph which is a straight line
linear equation: An equation with two variables (x and y) that takes the general form y = mx + b, where m is the slope of the line and b is the y-intercept
linear equation: a polynomial equation of the first degree
linear equation: An algebraic equation, such as y = 2x + 7 or 3x + 2y - z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables
linear equation: An equation of the form ax + b = 0 is a linear equation with x being the unknown variable For example, the equation 2x - 9 = 3 is a linear equation which can be re-written as 2x - 12 = 0
linear equation: in one variable can be written in the form Ax + B = C where A, B, and C are real numbers and A 0
linear equation: An equation containing linear expressions
nernst equation: Corrects standard electrode potentials for nonstandard conditions
nernst equation: used to calculate emf values at other than standard conditions
nernst equation: Describes the relationship between the potential of an electrochemical cell at any moment in time and the standard-state cell potential Used to under-stand what happens to the potential of a voltaic cell as it comes to equilibrium
nernst equation: A mathematical description of electrode behavior: E is the total potential, in millivolts, developed between the sensing and reference electrodes; Ex varies with the choice of electrodes, temperature, and pressure: 2 3RT/nF is the Nernst factor (R and F are constants, n is the charge on the ion, including sign, T is the temperature in degrees Kelvin), and ai is the activity of the ion to which the electrode is responding
nernst equation: The equation used to calculate the equilibrium potential for a permeant ion
ordinary differential equation: Equation containing derivatives of a function of a single variable. Its order is the order of the highest derivative it contains (e.g., a first-order differential equation involves only the first derivative of the function). Because the derivative is a rate of change, such an equation states how a function changes but does not specify the function itself. Given sufficient initial conditions, however, such as a specific function value, the function can be found by various methods, most based on integration
partial differential equation: A differential equation containing at least one partial derivative. In mathematics, an equation that contains partial derivatives, expressing a process of change that depends on more than one independent variable. It can be read as a statement about how a process evolves without specifying the formula defining the process. Given the initial state of the process (such as its size at time zero) and a description of how it is changing (i.e., the partial differential equation), its defining formula can be found by various methods, most based on integration. Important partial differential equations include the heat equation, the wave equation, and Laplace's equation, which are central to mathematical physics
partial differential equation: a differential equation involving a functions of more than one variable
personal equation: variability attributable to individual differences
quadratic equation: An equation in which one or more of the terms is squared but raised to no higher power, having the general form ax + bx + c = 0, where a, b, and c are constants. an equation such ax²+by+c = z, which includes numbers or quantities multiplied by themselves (quadratic from quadrate (14-21 centuries), from quadratus, past participle of quadrare ). Algebraic equation of particular importance in optimization. A more descriptive name is second-degree polynomial equation. Its standard form is ax^2 + bx + c = 0, and its solution is given by the quadratic formula
quadratic equation: equation in which one of the unknown quantities is squared (Mathematics)
quadratic equation: an equation in which the highest power of an unknown quantity is a square
regression equation: the equation representing the relation between selected values of one variable (x) and observed values of the other (y); it permits the prediction of the most probable values of y
schrodinger equation: the fundamental equation of wave mechanics
simple equation: mathematical comparison that is not complicated
simultaneous equation: set of two or more equations with variables and whose variables can be used to satisfy all equations in the set
trigonometric equation: equation that deals with the relation between sides and triangles
wave equation: a differential equation that describes the passage of harmonic waves through a medium