HOME TheInfoList picture info Mathematical Model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in the social sciences (such as economics, psychology, sociology, political science) [...More Info...]       [...Related Items...] Difference Equation In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms. The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation [...More Info...]       [...Related Items...] picture info Economist An economist is a practitioner in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy [...More Info...]       [...Related Items...] Mathematical Logic Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those. Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics [...More Info...]       [...Related Items...] picture info Physical Sciences Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences" [...More Info...]       [...Related Items...] picture info Defining Equation (physics) In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units. Constitutive Equation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or forces to strains or deformations. Some constitutive equations are simply phenomenological; others are derived from first principles [...More Info...]       [...Related Items...] Initial Condition In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables forward through time. In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time [...More Info...]       [...Related Items...] picture info Boundary Condition In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input [...More Info...]       [...Related Items...] picture info Kinematics Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on masses falls within kinetics. For further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies [...More Info...]       [...Related Items...] Statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors [...More Info...]       [...Related Items...] Variable (mathematics) In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them. The concept of a variable is also fundamental in calculus. Typically, a function y = f(x) involves two variables, y and x, representing respectively the value and the argument of the function [...More Info...]       [...Related Items...] Operator (mathematics) In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space. The most common operators are linear maps, which act on vector spaces. However, when using "linear operator" instead of "linear map", mathematicians often mean actions on vector spaces of functions, which also preserve other properties, such as continuity. For example, differentiation and indefinite integration are linear operators; operators that are built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol of a mathematical operation [...More Info...]       [...Related Items...] Parameter (computer Programming) In computer programming, a parameter (often called formal parameter or formal argument) is a special kind of variable, used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called actual arguments or actual parameters) with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters. Unlike argument in usual mathematical usage, the argument in computer science is thus the actual input expression passed/supplied to a function, procedure, or routine in the invokation/call statement, whereas the parameter is the variable inside the implementation of the subroutine [...More Info...]       [...Related Items...] Quantification (science) In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities [...More Info...]       [...Related Items...]