integrable
- adjective
- /ˈɪntɪɡrəbl/
- Specialized
:
integrable
- In calculus, an integrable function can be represented as the limit of Riemann sums.
- integrable systems
Where the resulting integrable functions form a Banach space, OK.
- Where the resulting integrable functions form a Banach space, OK.
- So integration by parts made this solvable, made it integrable like magic.
Examples
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In modern terminology, the former type of system is nonintegrable, and the latter is integrable.
Academic text (2005) -
A well-established technique known as the Weyl expansion shows that, to leading order in the system size, the same density of quantum energy levels exists for classically chaotic systems, such as the stadium billiard, as for integrable systems, such as the circular billiard.
Academic text (2005) -
Here it only applies if we're interested in the square integrable wave functions, which we are.
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So I'll just end with the completely integrable non linear equation.
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The system is integrable because angular momentum and energy are conserved, and every generic trajectory exhibits Einstein's regular type (a) motion.
Academic text (2005) -
A function is considered integrable if its integral can be calculated over a specific range.
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Calculating the area under the curve requires using an integrable function in the mathematical equations.
How Integrable
Surface Forms
Morphology
Etymology
Integrable comes from the Latin word integer, meaning 'whole', and from integrate, which means 'to make whole'. So in math, a function is integrable when you can add up its small parts to form a whole, like the area under a curve, which is why we can calculate its integral.