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Rouché's Theorem
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Geliefert zwischen Fr., 30.01.2026 und Mo., 02.02.2026
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, especially complex analysis, Rouché''s theorem, named after Eugène Rouché, tells us that if the complex-valued functions f and g are holomorphic inside and on some closed contour K, with g(z) f(z) on K, then f and f + g have the same number of zeros inside K, where each zero is counted as many times as its multiplicity. This theorem assumes that the contour K is simple, that is, without self-intersections. The theorem is usually used to simplify the problem of locating zeros, as follows. Given an analytic function, we write it as the sum of two parts, one of which is simpler and grows faster than (thus dominates) the other part. We can then locate the zeros by looking at only the dominating part. For example, the polynomial z5 + 3z3 + 7 has exactly 5 zeros in the disk z 2 since 3z3 + 7 32 = z5 for every z = 2, and z5, the dominating part, has five zeros in the disk.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131257667
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131257667
- Format Fachbuch
- Titel Rouché's Theorem
- Herausgeber Betascript Publishing
- Anzahl Seiten 72
- Genre Mathematik
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