Definitions for Nonlinear
non·lin·ear

Princeton's WordNetRate this definition:1.0 / 1 vote

1. nonlinearadjective

   designating or involving an equation whose terms are not of the first degree

GCIDERate this definition:1.0 / 2 votes

1. nonlinearadjective

   (Math.) Containing variables of greater than the first degree; -- of an equation. Opposite of linear.

2. nonlinearadjective

   (Physics) Represented by equations containing variables of greater than the first degree; -- of physical processes or relationships. Opposite of linear.

3. nonlinearadjective

   (Math.) Not depictable graphically as a straight line; not changing by a constant amount for each unit of time, distance, or other independent variable. Opposite of linear.

WiktionaryRate this definition:0.0 / 0 votes

1. nonlinearadjective

   not lying on a straight line

2. nonlinearadjective

   whose atoms do not lie in a straight line

3. nonlinearadjective

   having a product of independent variables, or a variable with an exponent not equal to one

4. nonlinearadjective

   whose output is not directly proportional to its input

5. nonlinearadjective

   erratic and unpredictable; tending to jump back and forth

   a film with a nonlinear plot

WikipediaRate this definition:0.0 / 0 votes

1. nonlinear

   In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in them. Systems can be defined as nonlinear, regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives, even if nonlinear in terms of the other variables appearing in it. As nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations (linearization). This works well up to some accuracy and some range for the input values, but some interesting phenomena such as solitons, chaos, and singularities are hidden by linearization. It follows that some aspects of the dynamic behavior of a nonlinear system can appear to be counterintuitive, unpredictable or even chaotic. Although such chaotic behavior may resemble random behavior, it is in fact not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology.

ChatGPTRate this definition:0.0 / 0 votes

1. nonlinear

   Nonlinear refers to a system, equation, or phenomenon in which the output or result is not directly proportional to the input. In such systems, small changes in input can lead to large changes in output, or the output might change in complex or unpredictable ways. It is a term often used in mathematics, physics, engineering, statistics, and other related fields.

The New Hacker's DictionaryRate this definition:5.0 / 1 vote

1. nonlinear

   [scientific computation] 1. Behaving in an erratic and unpredictable fashion; unstable. When used to describe the behavior of a machine or program, it suggests that said machine or program is being forced to run far outside of design specifications. This behavior may be induced by unreasonable inputs, or may be triggered when a more mundane bug sends the computation far off from its expected course. 2. When describing the behavior of a person, suggests a tantrum or a flame. “When you talk to Bob, don't mention the drug problem or he'll go nonlinear for hours.” In this context, go nonlinear connotes ‘blow up out of proportion’ (proportion connotes linearity).

Matched Categories

1. • Math

How to pronounce Nonlinear?

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How to say Nonlinear in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of Nonlinear in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of Nonlinear in Pythagorean Numerology is: 3

Examples of Nonlinear in a Sentence

1. Bate, Mueller & White, 1971, "Fundamentals of Astrodynamics":

   Equation (1.2-9) is a second order, nonlinear, vector, differential equation which has defied solution in its present form. It is here therefore we depart from the realities of nature to make some simplifying assumptions...

2. Neil Gershenfeld:

   For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That's a linear response. If you hit a person twice as hard they're unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork.

3. Field Museum senior research scientist:

   There’s more than one way to make magenta with iridescence, the parent species each have their own way of making magenta, which is, I think, why you can have this nonlinear or surprising outcome when you mix together those two recipes for producing a feather color.

4. Greg Schmidt:

   My dad invited Rudy Kalman to give a lecture at Ames, and when he did, Dad had an epiphany, rudy Kalman had written a paper about a theoretical' linear' solution to estimating a vehicle's location and speed. The problem was that this was a fundamentally' nonlinear' problem ; that's like the difference in complexity between floating down a lazy river and going over a waterfall, where your motion becomes chaotic and unpredictable. My dad then developed the equations for how to solve this nonlinear problem -- a major extension of Kalman's work.

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=Nonlinear
2. ^ GCIDE
   https://gcide.gnu.org.ua/?q=Nonlinear
3. ^ Wiktionary
   https://en.wiktionary.org/wiki/Nonlinear
4. ^ Wikipedia
   https://en.wikipedia.org/wiki/Nonlinear
5. ^ ChatGPT
   https://chat.openai.com
6. ^ The New Hacker's Dictionary
   https://www.gutenberg.org/files/3008/3008-h/3008-h.htm#Nonlinear