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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 193

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Year 0·Month 7·Week 4

Day 193: Asymptotic Methods and Saddle Points

Day 193 of 2,016~6 min read

Learning Objectives

•Apply the saddle point approximation to integrals
•Find steepest descent paths through saddle points
•Evaluate integrals with large parameters asymptotically
•Connect to WKB approximation in quantum mechanics
•Understand Stokes phenomenon and asymptotic series
•Apply to partition functions and path integrals

Today's Schedule (7 hours)

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1 The Problem Large Parameter Integrals 2 Saddle Point Stationary Phase Method 3 Method of Steepest Descent 4 The Saddle Point Formula 5 Example Stirlings Formula 6 WKB from Saddle Points 7 Stokes Phenomenon

Day 192Day 193 of 2,016Day 194