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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 173

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Year 0·Month 7·Week 1

Day 173: Conformal Mappings — Angle-Preserving Transformations

Day 173 of 2,016~12 min read

Learning Objectives

•Define conformal mappings and their geometric properties
•Prove that analytic functions with nonzero derivative are conformal
•Work with Möbius (linear fractional) transformations
•Map between standard domains (disk, half-plane, strip)
•Introduce the Schwarz-Christoffel transformation
•Apply conformal mapping to physics problems

Today's Schedule (7 hours)

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1 Definition and Geometric Meaning 2 Local Behavior of Conformal Maps 3 Mbius Transformations 4 Standard Mappings 5 Schwarz-Christoffel Transformation Introduction 6 Applications in Physics 7 Quantum Mechanics Connection

Day 172Day 173 of 2,016Day 174