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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 183

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Year 0·Month 7·Week 3

Day 183: Laurent Series

Day 183 of 2,016~9 min read

Learning Objectives

•Define and construct Laurent series expansions
•Understand the annulus of convergence
•Compute Laurent series using various techniques
•Identify the principal part and analytic part
•Relate Laurent series to singularity classification
•Connect to quantum mechanical expansions

Today's Schedule (7 hours)

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On this page

1 Motivation Beyond Taylor Series 2 Laurent Series Definition 3 Parts of the Laurent Series 4 Computing Laurent Series Method 1 Direct Coefficient Formula Method 2 Algebraic Manipulation Method 3 Known Expansions Method 4 Partial Fractions 5 Uniqueness of Laurent Series 6 Annulus of Convergence Quantum Mechanics Connection Perturbation Theory Greens Function Expansion S-Matrix Poles

Day 182Day 183 of 2,016Day 184