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In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function (s) and involves the derivatives of those functions. [ 1 ]
An ode (from Ancient Greek: ᾠδή, romanized: ōidḗ) is a type of lyric poetry, with its origins in Ancient Greece.Odes are elaborately structured poems praising or glorifying an event or individual, describing nature intellectually as well as emotionally.
In mathematics, 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), ..., a n (x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y (n) are the successive derivatives of an unknown function y of ...
For example, the second-order equation y′′ = −y can be rewritten as two first-order equations: y′ = z and z′ = −y. In this section, we describe numerical methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution y at more than one ...
Ode–Several stanzaic forms that are more complex than that of the lyric. It is embedded with intricate rhyme schemes and an irregular number of lines of considerable length. Written with a rich and intense expression, an ode is structured to deliver an elevated thought to praise a person or object. “Ode to a Nightingale” is an example.
Also apophthegm. A terse, pithy saying, akin to a proverb, maxim, or aphorism. aposiopesis A rhetorical device in which speech is broken off abruptly and the sentence is left unfinished. apostrophe A figure of speech in which a speaker breaks off from addressing the audience (e.g., in a play) and directs speech to a third party such as an opposing litigant or some other individual, sometimes ...
In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems .
It is a pastoral elegy, in the English tradition of John Milton's Lycidas. [1] Shelley had studied and translated classical elegies. The title of the poem is modelled on ancient works, such as Achilleis (a poem about Achilles ), an epic poem by the 1st-century AD Roman poet Statius , and refers to the untimely death of the Greek Adonis , a god ...