Laplace's Coefficients

Laplace's Coefficients
Harmonic Har*mon"ic (h[aum]r*m[o^]n"[i^]k), Harmonical Har*mon"ic*al (-[i^]*kal), a. [L. harmonicus, Gr. "armoniko`s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster]

Harmonic twang! of leather, horn, and brass. --Pope. [1913 Webster]

2. (Mus.) Relating to harmony, -- as melodic relates to melody; harmonious; esp., relating to the accessory sounds or overtones which accompany the predominant and apparent single tone of any string or sonorous body. [1913 Webster]

3. (Math.) Having relations or properties bearing some resemblance to those of musical consonances; -- said of certain numbers, ratios, proportions, points, lines, motions, and the like. [1913 Webster]

{Harmonic interval} (Mus.), the distance between two notes of a chord, or two consonant notes.

{Harmonical mean} (Arith. & Alg.), certain relations of numbers and quantities, which bear an analogy to musical consonances.

{Harmonic motion}, the motion of the point A, of the foot of the perpendicular PA, when P moves uniformly in the circumference of a circle, and PA is drawn perpendicularly upon a fixed diameter of the circle. This is simple harmonic motion. The combinations, in any way, of two or more simple harmonic motions, make other kinds of harmonic motion. The motion of the pendulum bob of a clock is approximately simple harmonic motion.

{Harmonic proportion}. See under {Proportion}.

{Harmonic series} or {Harmonic progression}. See under {Progression}.

{Spherical harmonic analysis}, a mathematical method, sometimes referred to as that of {Laplace's Coefficients}, which has for its object the expression of an arbitrary, periodic function of two independent variables, in the proper form for a large class of physical problems, involving arbitrary data, over a spherical surface, and the deduction of solutions for every point of space. The functions employed in this method are called spherical harmonic functions. --Thomson & Tait.

{Harmonic suture} (Anat.), an articulation by simple apposition of comparatively smooth surfaces or edges, as between the two superior maxillary bones in man; -- called also {harmonia}, and {harmony}.

{Harmonic triad} (Mus.), the chord of a note with its third and fifth; the common chord. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

Look at other dictionaries:

  • Laplace's equation — In mathematics, Laplace s equation is a partial differential equation named after Pierre Simon Laplace who first studied its properties. The solutions of Laplace s equation are important in many fields of science, notably the fields of… …   Wikipedia

  • LAPLACE (P. S. de) — Fils d’un cultivateur, auquel l’étude fut ouverte, Laplace dut à des talents remarquables en mathématiques de s’imposer au monde savant dès les dernières années de l’Ancien Régime. Mais c’est à travers la Révolution, l’Empire et la Restauration,… …   Encyclopédie Universelle

  • Laplace operator — This article is about the mathematical operator. For the Laplace probability distribution, see Laplace distribution. For graph theoretical notion, see Laplacian matrix. Del Squared redirects here. For other uses, see Del Squared (disambiguation) …   Wikipedia

  • Laplace invariant — In differential equations, the Laplace invariant of any of certain differential operators is a certain function of the coefficients and their derivatives. Consider a bivariate hyperbolic differential operator of the second order:partial x ,… …   Wikipedia

  • Laplace transform — Math. a map of a function, as a signal, defined esp. for positive real values, as time greater than zero, into another domain where the function is represented as a sum of exponentials. Cf. Fourier transform. [1940 45; after P. S. LAPLACE] * * *… …   Universalium

  • laplace transform — ləˈpläs , las noun Usage: usually capitalized L Etymology: after Pierre Simon de Laplace died 1827 French astronomer and mathematician : a transformation of a function f(x) into the function g(t) = ∫0∞ e xt f(x) dx that is useful especially in… …   Useful english dictionary

  • Pierre-Simon Laplace — Laplace redirects here. For the city in Louisiana, see LaPlace, Louisiana. For the joint NASA ESA space mission, see Europa Jupiter System Mission. Pierre Simon, marquis de Laplace Pierre Simon Laplace (1749–1827). Posthumous portrait …   Wikipedia

  • Transformation de Laplace — Transformée de Laplace Pour les articles homonymes, voir Laplace. Sommaire 1 Définition 2 Inversion 3 Propriétés …   Wikipédia en Français

  • Transformee de Laplace — Transformée de Laplace Pour les articles homonymes, voir Laplace. Sommaire 1 Définition 2 Inversion 3 Propriétés …   Wikipédia en Français

  • Transformée de Laplace — Pour les articles homonymes, voir Laplace. Sommaire 1 Définition 2 Inversion 3 Propriétés …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”