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ERIC Number: EJ1163207
Record Type: Journal
Publication Date: 2017
Pages: 13
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1051-1970
Unpacking Rouché's Theorem
Howell, Russell W.; Schrohe, Elmar
PRIMUS, v27 n8-9 p801-813 2017
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the conclusion of Rouché's Theorem, but most undergraduate texts give no geometric insights that lead to an understanding of "why" Rouché's Theorem holds. In addition, most texts do not inform students that a stronger version of the theorem exists. In this paper we present a simplified proof of the stronger version, which is a suitable topic for students to pursue as a short project, and provide a geometric argument for the weaker version. Finally, as a project for advanced students, we unpack a standard application of this theorem as used in control systems: the Nyquist stability criterion.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A