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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 138

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Year 0·Month 5·Week 4

Day 138: Argument Principle & Rouché's Theorem

Day 138 of 2,016~14 min read

Learning Objectives

•State and prove the Argument Principle
•Count zeros and poles using contour integrals
•Apply Rouché's theorem to locate zeros
•Understand the winding number concept
•Apply these theorems to prove the Fundamental Theorem of Algebra
•Connect to physics applications (Nyquist stability criterion)

Today's Schedule (7 hours)

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On this page

1 The Argument Principle 2 Proof of the Argument Principle 3 The Winding Number 4 Rouchs Theorem 5 Applications of Rouchs Theorem 6 The Open Mapping Theorem 7 Quantum Mechanics Physics Connections

Day 137Day 138 of 2,016Day 139