1) "Linear" -- As to linear programming
lin·e·ar
Pronunciation: 'li-nE-&r
Function: adjective
1 a (1) : of, relating to, resembling, or having a graph that is a line and especially a straight line : STRAIGHT (2) : involving a single dimension b (1) : of the first degree with respect to one or more variables (2) : of, relating to, based on, or being linear equations, linear differential equations, linear functions, linear transformations, or linear algebra c (1) : characterized by an emphasis on line <linear art> (2) : composed of simply drawn lines with little attempt at pictorial representation <linear script> d : consisting of a straight chain of atoms
2 : elongated with nearly parallel sides <linear leaf> -- see LEAF illustration
3 : having or being a response or output that is directly proportional to the input
4 : of, relating to, or based or depending on sequential development <linear thinking> <a linear narrative>
- lin·e·ar·i·ty /"li-nE-'er-&-tE, -'a-r&-/ noun
- lin·e·ar·ly /'li-nE-&r-lE/ adverb
Pronunciation Symbols

The word linear comes from the Latin word linearis, which means created by lines. In mathematics, a linear function f(x) is one which satisfies the following two properties (but see below for a slightly different usage of the term):

Additivity property (also called the superposition property): f(x + y) = f(x) + f(y). This says that f is a group homomorphism with respect to addition.

Homogeneity property: f(Î±x) = Î±f(x) for all Î±. It turns out that homogeneity follows from the additivity property in all cases where Î± is rational. In that case if the linear function is continuous, homogeneity is not an additional axiom to establish if the additivity property is established.

In this definition, x is not necessarily a real number, but can in general be a member of any vector space.

The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian. When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.

Nonlinear equations and functions are of interest to physicists and mathematicians because they are hard to solve and give rise to interesting phenomena such as chaos.

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations.

See also: linear element, linear system, nonlinearity.

1 Integral Linearity

2 Linear polynomials

3 Physics

4 Electronics

5 Military tactical formations

6 Music

2) "Programming" -- As to linear programming
²program
Variant(s): also programme
Function: transitive verb
Inflected Form(s): -grammed or -gramed; -gram·ming or -gram·ing
1 a : to arrange or furnish a program of or for : BILL b : to enter in a program
2 : to work out a sequence of operations to be performed by (a mechanism) : provide with a program
3 a : to insert a program for (a particular action) into or as if into a mechanism b : to control by or as if by a program c (1) : to code in an organism's program (2) : to provide with a biological program <cells programmed to synthesize hemoglobin>
4 : to predetermine the thinking, behavior, or operations of as if by computer programming <children are programmed into violence -- Lisa A. Richette>
- pro·gram·ma·bil·i·ty /(")prO-"gra-m&-'bi-l&-tE/ noun
- pro·gram·ma·ble /'prO-"gra-m&-b&l/ adjective or noun
Pronunciation Symbols

Software Development Process

This article is part of the Software Development Process series

Activities and Steps

Requirements | Architecture | Implementation | Testing | Deployment

Models

Agile | Cleanroom | Iterative | RAD | RUP | Spiral | Waterfall | XP

Supporting Disciplines

Configuration Management | Documentation | Project Management | User Experience Design

Computer programming (often shortened to programming or coding) is the process of writing, testing, and maintaining the source code of computer programs. The source code is written in a programming language. This code may be a modification of existing source or something completely new. The process of writing source code requires expertise in many different subjects, including knowledge of the application domain and algorithms to implement the desired behavior. Within software engineering, programming (the implementation) is regarded as one phase in a software development process.

In some specialist applications or extreme situations a program may be written or modified (known as patching) by directly storing the numeric values of the machine code instructions to be executed into memory.

There is an ongoing debate on the extent to which the writing of programs is an art, a craft or an engineering discipline.^[1]

Another ongoing debate is the extent to which the programming language used in writing programs affects the form that the final program takes. This debate is analogous to that surrounding the Sapir Whorf hypothesis in linguistics.^{[citation needed]}

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Further Data On Term for linear programming
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