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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 134

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Year 0·Month 5·Week 4

Day 134: Laurent Series — Expanding Around Singularities

Day 134 of 2,016~11 min read

Learning Objectives

•Understand why Taylor series fail at singularities
•Derive and compute Laurent series expansions
•Identify the principal part and analytic part
•Determine the annulus of convergence
•Extract residues from Laurent series
•Connect to physics: multipole expansions

Today's Schedule (7 hours)

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1 Motivation When Taylor Series Fail 2 Laurent Series Definition 3 Computing Laurent Series 4 Examples 5 Different Annuli Different Series 6 The Residue 7 Physics Connection Multipole Expansions

Day 133Day 134 of 2,016Day 135