Real Analysis (2015-2025) | PYQ Discussion | TARGET MH SET 2026 | LEC 02 | IFAS

Real Analysis (2015-2025) | PYQ Discussion | TARGET MH SET 2026 explained with clear concepts and exam-focused approach. Master analytic functions, harmonic conjugates, singularities (removable/pole/essential), conformal mapping, and power series radius of convergence. Includes MH SET previous year questions, problem-solving tricks for CSIR NET & SET. 🔥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 Real Analysis (2015-2025) | PYQ Discussion [00:05:59] – Q2: Stereographic Projection [00:08:25] – Q3: Analytic Function Existence (True/False) [00:10:26] – Concept: Harmonic Conjugate [00:14:57] – Q4: Singularity at z=0 [00:15:20] – Answer: Removable Singularity [00:19:00] – Q5: Contour Integration (sinz) [00:25:16] – Q6: Radius of Convergence (Not 1) [00:32:56] – Q7: Constant Analytic Function [00:37:09] – Q8: Conformal on Unit Disc [00:43:42] – Q9: Entire Function Zeros (False) [00:45:22] – Trick: Identity Theorem Application [00:50:44] – Q10: Non‑zero Analytic Function [00:52:09] – Summary & Crash Course Info [00:53:45] – Complete Session (Real Analysis (2015-2025) | PYQ Discussion) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Analytic functions & Cauchy-Riemann equations • Harmonic conjugates & entire functions • Singularities – removable, pole, essential • Conformal mapping on unit disk • Power series – radius of convergence • Residue theorem & contour integration ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on Real Analysis PYQs (2015-2025) for MH SET 2026 – covering complex analysis essentials. Key concepts: analyticity via Cauchy-Riemann equations, harmonic conjugate existence, removable singularities (e.g., sinz/(1-e^z) at z=0), conformal mapping condition (f'(z)≠0), radius of convergence calculation (root/ratio test), residue theorem applications, and identity theorem for analytic functions. Exam-oriented problem-solving on real analysis with counterexamples (entire functions with infinite zeros, identity theorem constraints) covered. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 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   #realanalysispyqdiscussion #targetmhset2026 #analyticfunctions #harmonicconjugates #singularities #conformalmapping #powerseries #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetjune2026 #csirnetlecture #ifasmathematics