equation (redirected from equation of the second order)

equation, in mathematics, a statement, usually written in symbols, that states the equality of two quantities or algebraic expressions, e.g., x+3=5. The quantity x+3, to the left of the equals sign (=), is called the left-hand, or first, member of the equation, that to the right (5) the right-hand, or second, member. A numerical equation is one containing only numbers, e.g., 2+3=5. A literal equation is one that, like the first example, contains some letters (representing unknowns or variables). An identical equation is a literal equation that is true for every value of the variable, e.g., the equation (x+1)²=x²+2x+1. A conditional equation (usually referred to simply as an equation) is a literal equation that is not true for all values of the variable, e.g., only the value 2 for x makes true the equation x+3=5. To solve an equation is to find the value or values of the variable that satisfy it. Polynomial equations, containing more than one term, are classified according to the highest degree of the variable they contain. Thus the first example is a first degree (also called linear) equation. The equation ax²+bx+c=0 is a second degree, or quadratic, equation in the unknown x if the letters a, b, and c are assumed to represent constants. In algebra, methods are evolved for solving various types of equations. To be valid the solution must satisfy the equation. Whether it does can be ascertained by substituting the supposed solution for the variable in the equation. The simultaneous solution of two or more equations is a set of values of the variables that satisfies each of the equations. In order that a solution may exist, the number of equations (i.e., conditions) must generally be no greater than the number of variables. In chemistry an equation (see chemical equation) is used to represent a reaction.

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equation

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.

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equation

An arithmetic expression that equates one set of conditions to another; for example, A = B + C. In a programming language, assignment statements take the form of an equation. The above example assigns the sum of B and C to the variable A.

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equation

1. a mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots)

2. See chemical equation

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equation [i′kwā·zhən]

(chemistry)

A symbolic expression that represents in an abbreviated form the laboratory observations of a chemical change; an equation (such as 2H₂+ O₂→ 2H₂O) indicates what reactants are consumed (H₂and O₂) and what products are formed (H₂O), the correct formula of each reactant and product, and satisfies the law of conservation of atoms in that the symbols for the number of atoms reacting equals the number of atoms in the products.

(mathematics)

A statement that each of two expressions is equal to the other.