Search results
Results from the WOW.Com Content Network
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, 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 ]
This ode is an invocation to Apollo, begging help and inspiration for this important task. IV.7, Diffugere nives, redeunt iam... – The Lesson of Spring's Return – An ode on the same springtime theme as I.4 – Addressed to his friend Torquatus. Though the earth renews itself, and the waning moon waxes afresh, yet death is the ending of ...
An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y), which, therefore, depends on x. Thus x is often called the independent variable of the equation.
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 ...
(Figure 2) Illustration of numerical integration for the equation ′ =, = Blue is the Euler method; green, the midpoint method; red, the exact solution, =. The step size is =
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1
In Latin poetry the epode was cultivated, in conscious archaism, both as a part of the ode and as an independent branch of poetry. Of the former class, the epithalamia of Catullus , founded on an imitation of Pindar , present us with examples of strophe, antistrophe and epode; and it has been observed that the celebrated ode 1.12 of Horace ...