Complex Integration Part 2: Cauchy Residue Theorem & Laurent Series | Lecture 3 | No Backlog

Welcome to Lecture 3 (Part 2) of Complex Integration on No Backlog! 📚 In this lecture, we cover Singular Points, Poles of simple/higher orders, Shortcuts to find Residues, Cauchy-Residue Theorem, and Laurent Series expansion for semester exams (B.Tech / B.E, B.Sc, GATE). 📌 Timestamps & Topics Covered in Lecture 3: 00:00 - Introduction & Singular Points of f(z) 02:15 - How to find Poles (Simple Pole vs Pole of Order m) 05:30 - Shortcut Methods for Finding Residues (Case 1 & Case 2) 10:45 - Solved Example: Residue of f(z) = (12z - 7) / [(z - 1)²(2z + 3)] 15:20 - Cauchy Residue Theorem Statement & Formula [∮ f(z) dz = 2πi ∑R] 19:10 - Important Exam Questions on Circular & Figure-8 Contours 24:30 - Laurent Series Expansion & Principal Part (Taylor vs Laurent vs Fourier) 💡 Download Notes & Formula Sheet: https://t.me/nobacklogyoutubechannel ⏮️ Watch Lecture 2 (Part 1 - Line Integrals & Cauchy Theorem) Here:    • Complex Integration Part 1: Cartesian & Po...   🔔 Subscribe to 'No Backlog' to clear your university exams with zero stress! #ComplexIntegration #CauchyResidueTheorem #LaurentSeries #EngineeringMathematics #ComplexAnalysis #BTechMaths #NoBacklog