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Partial differentials

Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone.

Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone.

Partial differential

Differential Dif`fer*en"tial, n. 1. (Math.) An increment, usually an indefinitely small one, which is given to a variable quantity. Note: According to the more modern writers upon the differential and integral calculus, if two or more quantities are dependent on each other, and subject to increments of value, their differentials need not be small, but are any quantities whose ratios to each other are the limits to which the ratios of the increments approximate, as these increments are reduced nearer and nearer to zero. 2. A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities. 3. (Elec.) (a) One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other. (b) A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all. --Knight. Partial differential (Math.), the differential of a function of two or more variables, when only one of the variables receives an increment. Total differential (Math.), the differential of a function of two or more variables, when each of the variables receives an increment. The total differential of the function is the sum of all the partial differentials.

Differential Dif`fer*en"tial, n. 1. (Math.) An increment, usually an indefinitely small one, which is given to a variable quantity. Note: According to the more modern writers upon the differential and integral calculus, if two or more quantities are dependent on each other, and subject to increments of value, their differentials need not be small, but are any quantities whose ratios to each other are the limits to which the ratios of the increments approximate, as these increments are reduced nearer and nearer to zero. 2. A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities. 3. (Elec.) (a) One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other. (b) A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all. --Knight. Partial differential (Math.), the differential of a function of two or more variables, when only one of the variables receives an increment. Total differential (Math.), the differential of a function of two or more variables, when each of the variables receives an increment. The total differential of the function is the sum of all the partial differentials.

- In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable...

- variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f ( x ...

- In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

- In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion...

- A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

- {\displaystyle {\frac {\partial u}{\partial t}}=6u{\frac {\partial u}{\partial x}}-{\frac {\partial ^{3}u}{\partial x^{3}}}.} Solving differential equations is not...

- physical use of infinitesimal differentials with the mathematical impossibility of them as follows. The differentials represent finite non-zero values...

- See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

- of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...

- D_{j}=-i{\frac {\partial }{\partial x_{j}}}} or sometimes, D j = ∂ ∂ x j {\textstyle D_{j}={\frac {\partial }{\partial x_{j}}}} . The most common differential operator...

- variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f ( x ...

- In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

- In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion...

- A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

- {\displaystyle {\frac {\partial u}{\partial t}}=6u{\frac {\partial u}{\partial x}}-{\frac {\partial ^{3}u}{\partial x^{3}}}.} Solving differential equations is not...

- physical use of infinitesimal differentials with the mathematical impossibility of them as follows. The differentials represent finite non-zero values...

- See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

- of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...

- D_{j}=-i{\frac {\partial }{\partial x_{j}}}} or sometimes, D j = ∂ ∂ x j {\textstyle D_{j}={\frac {\partial }{\partial x_{j}}}} . The most common differential operator...

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