# Partial fractions

Also found in: Encyclopedia, Wikipedia.

(Alg.) | fractions whose sum equals a given fraction. |

See also: partial

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.

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Also found in: Encyclopedia, Wikipedia.

(Alg.) | fractions whose sum equals a given fraction. |

See also: partial

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.

One may finally obtain the rth (1 [less than or equal to] r [less than or equal to] m) component of [W.sup.*.sub.F](s) using partial fractions as follows:

It may be remarked here that while making partial fractions, we have assumed that the roots [[bar.s].sub.ij] are distinct.

3.5c] through partial fractions and Gould Hsu inverse series relations [6].

Generally, the synthesis of vibrating mechanical systems comes down to the prime factorization of the characteristic function (decomposition into partial fractions, decomposition into continued fractions).

In extreme cases, it is the sum of partial fractions or a continued fraction of the analyzed dynamic characteristic [Y.sub.U](s) or [Z.sub.U](s) describing the dynamic properties.

There are three appendices, Partial fractions, Laplace Transforms Definitions and Derivations, and Series Solutions of ODEs.

Sivazlian, "Partial fractions expansion: a review of computational methodology and efficiency," Journal of Computational and Applied Mathematics, vol.

Slota, "Partial fractions decompositions of some rational functions," Applied Mathematics and Computation, vol.

This edition has been expanded to include chapters on: integral equations, calculus of variations, tensor analysis, time series, and partial fractions. Many new exercises and solutions are also provided.

We decompose this into partial fractions so that the coefficients of [z.sup.n] can be obtained:

Next substituting u = 1 and using partial fractions we obtain

To solve this we decompose p([[lambda]).sup.-1] into partial fractions

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