Definition of Partial fractions. Meaning of Partial fractions. Synonyms of Partial fractions

Here you will find one or more explanations in English for the word Partial fractions. Also in the bottom left of the page several parts of wikipedia pages related to the word Partial fractions and, of course, Partial fractions synonyms and on the right images related to the word Partial fractions.

Definition of Partial fractions

Partial fractions
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 fraction
Fraction Frac"tion, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.] 1. The act of breaking, or state of being broken, especially by violence. [Obs.] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. 2. A portion; a fragment. Some niggard fractions of an hour. --Tennyson. 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. Common, or Vulgar, fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator.

Meaning of Partial fractions from wikipedia

- the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. The importance of the partial fraction decomposition...
- analytic theory of continued fractions. If one of the partial numerators an+1 is zero, the infinite continued fraction b 0 + K ∞ i = 1 a i b i {\displaystyle...
- {L}}^{-1}\{H(s)\}.} Partial fraction expansion To evaluate this inverse transform, we begin by expanding H(s) using the method of partial fraction expansion, 1...
- {\partial G}{\partial x_{2}}}\right)_{\frac {x_{1}}{x_{3}}}} Express mole fractions of a component as functions of other components' mole fraction and...
- of the day." Barrow's proof of the result was the earliest use of partial fractions in integration. Adapted to modern notation, Barrow's proof began as...
- this reduces to the usual method of partial fractions. By using polynomial long division and the partial fraction technique from algebra, any rational...
- {x+2}}{x^{2}-3}}} . Algebraic fractions are subject to the same laws as arithmetic fractions. A rational fraction is an algebraic fraction whose numerator and denominator...
- expressing a proper rational fraction as the sum of two or more fractions is called resolving it into partial fractions. For example, 2 x x 2 − 1 = 1...
- rational fractions with integer coefficients. The term partial fraction is used when decomposing rational fractions into sums of simpler fractions. For example...
- Differentiation under the integral sign Trigonometric substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Trapezium...