Singularity | Complex Analysis | CSIR NET | SET | GATE Mathematics | Lec-5 | IFAS

Singularity in Complex Analysis explained with clear concepts and exam-focused approach. This session covers essential isolated and non-isolated singularities, crucial for CSIR NET Mathematics, SET, and GATE Mathematics. Master the definition of singular points, limit point logic, and classification with powerful PYQ problem-solving tricks that help you tackle tricky questions instantly. Perfect for building a strong conceptual foundation for competitive exams. 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/mathe... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00:00] – Introduction of Singularity | Complex Analysis [00:01:54] – Recap: Analytic Functions & CR Equations [00:07:47] – Introduction: Singularities [00:08:06] – Concept: Regular Point vs Singular Point [00:11:13] – Definition: Singular Point (Limit Point) [00:13:09] – Example: f(z)=1/z – Singular Set [00:15:18] – Question 1: f(z)=1/z – True Statements [00:18:36] – Question 2: Essential Singularity at 0 [00:27:10] – Question 3: sin(z)/z, f(0)=1 – Regular [00:31:36] – Classification: Isolated & Non-Isolated [00:33:45] – Isolated Singularity: Definition [00:37:25] – Non-Isolated Singularity: Definition [00:38:44] – Important: Limit Point via Sequence/Nbhd [00:42:33] – Isolated: Deleted Nbhd Analytic [00:44:49] – Example: z/sin z – Isolated at nπ [00:47:16] – Question 4: z/sin z – True Statements [00:48:15] – Question 5: cosec(1/z) – Non-Isolated 0 [00:55:36] – Question 6: 1/sin(πz) – All Isolated Integers [00:58:11] – Trick: Finite Singularities = All Isolated [00:58:56] – Question 7: tan(1/z) – Non-Isolated 0 [01:03:19] – Question 8: sin(1/z) – Singularities [01:05:14] – Homework: Meromorphic Function Singularities [01:08:49] – Complete Session (Singularities & Classification) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Singular Point vs Regular Point Definition • Isolated Singularity Concept & Identification Tricks • Non-Isolated Singularity & Limit Point of Singularities • PYQ Problems on 1/z, sinz/z, cosec(1/z), tan(1/z) • Classification of Singularities – Key Concepts • CSIR NET/SET/GATE Important Questions & Problem-Solving ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on the fundamental concept of Singularity in Complex Analysis. Key definitions, including the difference between isolated and non-isolated singularities, are explained with limit point logic and clear examples like 1/z and sinz/z. Problem-solving approaches for PYQs on cosec(1/z), tan(1/z) are demonstrated, highlighting identification tricks and common exam traps. The session reinforces how to determine whether a Singularity is isolated or non-isolated, ensuring you are well-prepared for CSIR NET, SET, and GATE questions. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics ✅ TIFR Mathematics ✅ PhD Entrance Exams ━━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for CSIR NET & GATE Mathematics? (Our Results Speak): ✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....) ✅ CSIR NET June 2025: 4200+ Selections (AIR 1, 2, 6, 10...) ✅ CSIR NET Dec 2024: 4000+ Selections (AIR 5, 6, 7, 8, 9...) ✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...) ✅ CSIR NET Dec 2023: 1200+ Selections (AIR 2, 4, 5...) 📄 View IFAS Result Sheet: 👉 https://drive.google.com/file/d/1THh6... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 📘 Free Counselling: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥CSIR NET Mathematical Science Live & Recorded Course: https://ifasonline.com/csir-net/mathe... 🎯 GATE Mathematics Recorded Course: https://ifasonline.com/gate/mathemati... 📘CSIR NET Mathematical Science Books: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 Download IFAS App: Android: https://play.google.com/store/apps/de... IOS: https://apps.apple.com/us/app/ifas/id... ━━━━━━━━━━━━━━━━━━━━━━━━━ Stay Updated Via Other Social Media: ✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu... ✔Instagram:   / csir_net_mathematical_science   #singularityincomplexanalysis #isolatedsingularity #nonisolatedsingularity #csirnetmathematics #complexanalysis #pyqproblemsolving #regularpoint #limitpoint #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetjune2026 #csirnetlecture #ifasmathematics