Analytic Functions | Complex Analysis | CSIR NET | SET | Gate Mathematics | Lec-3 | IFAS

Analytic Functions | Complex Analysis | CSIR NET | SET | Gate Mathematics | Lec-3 | IFAS explained with clear concepts and exam-focused approach. Covers analytic functions, Cauchy-Riemann equations, regular points, and harmonic functions with PYQ-based tricks for CSIR NET, SET, GATE aspirants seeking conceptual clarity and problem-solving shortcuts. 🔥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 to Analytic Functions [00:04:28] – Concept: Cauchy‑Riemann (CR) Equations [00:06:07] – Concept: CR in Polar Form (Trick) [00:13:25] – Important: Necessary vs Sufficient (CR) [00:17:57] – Question: CR for f(z)=√z (Polar) [00:24:00] – Question: Sufficient Condition for Diff. [00:26:04] – Concept: Regular Point & Analyticity [00:31:12] – Trick: Regular Point Definition [00:43:57] – Question: Property of Regular Point [00:47:20] – Concept: Analytic Function Definition [00:48:42] – Concept: Entire Function [00:51:08] – Question: Identifying Entire Functions [00:53:36] – Trick: f(z)=z̄ is Nowhere Differentiable [00:55:14] – Question: z² sin(1/z) Continuity [01:05:23] – Concept: Harmonic Function (Laplacian) [01:06:36] – Question: Identify Harmonic Functions [01:10:18] – Complete Session (Analytic Functions) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Cauchy-Riemann Equations (Cartesian, Polar, z-bar Form) • Necessary & Sufficient Condition for Differentiability • Regular Point & Analytic Function Concepts • Entire Function & Examples • Harmonic Function & Laplace Equation • PYQ-Based Analytic Function Problem-Solving Tricks ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on Analytic Functions in Complex Analysis, covering CR equations, regular points, entire functions, and harmonic functions. Problem-solving tricks and PYQs from CSIR NET, SET, GATE are demonstrated with clear derivations. The session builds conceptual depth on Analytic Functions, emphasizing shortcuts and exam-focused approach for mastering analyticity and differentiability. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 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   #analyticfunctions #complexanalysis #complexfunction #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetjune2026 #csirnetlecture #ifasmathematics