EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Equation solvingIn mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Algebraic equationIn mathematics, an algebraic equation or polynomial equation is an equation of the form where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation.
QuantityQuantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties. Quantity is among the basic classes of things along with quality, substance, change, and relation.
Physical quantityA physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Following ISO 80000-1, any value or magnitude of a physical quantity is expressed as a comparison to a unit of that quantity.
System of polynomial equationsA system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of complex numbers, because each solution belongs to a field extension of k, which is isomorphic to a subfield of the complex numbers.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
Quadratic equationIn algebra, a quadratic equation () is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.
Functional equationIn mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates several values of the same function.
Dimensionless quantityA dimensionless quantity (also known as a bare quantity, pure quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). The corresponding unit of measurement is one (symbol 1), which is not explicitly shown.
Steffensen's methodIn numerical analysis, Steffensen's method is an iterative method for root-finding named after Johan Frederik Steffensen which is similar to Newton's method, but with certain situational advantages. In particular, Steffensen's method achieves similar quadratic convergence, but without using derivatives as Newton's method does.
