Master Analytic Functions in 1 Hour!| CSIR NET, MH-SET

In this lecture: You will learn the complete theory of Analytic Functions, regular points, Milne-Thomson method, and how to instantly solve Complex Analysis questions for competitive exams. Topics covered: `[00:00:11]` — Introduction to Regular Points & Differentiability `[00:04:59]` — Conceptual Examples on Regularity of Functions `[00:13:35]` — Rigorous Definition of Analytic Functions (Global vs Local) `[00:17:54]` — Understanding Entire Functions & Special Cases `[00:20:22]` — Introduction to Harmonic Functions & Laplace Equation `[00:25:56]` — Fundamental Properties of Analytic Functions & Harmonic Conjugates `[00:32:02]` — Theorems on Constant Analytic Functions `[00:37:01]` — Open Mapping Theorem & Orthogonal Families of Curves `[00:46:15]` — Milne-Thomson Method for Constructing Analytic Functions `[00:53:15]` — Practice Problems on Milne-Thomson Method using Bernoulli's Rule `[00:58:49]` — Key takeaways & Homework Announcement This video covers Analytic Functions and Milne-Thomson Method for CSIR NET June 2026 / IIT JAM 2027 / MH-SET 2026]. It dives deep into regular points, harmonic conjugates, Cauchy-Riemann equations, and standard short tricks to determine when an analytic function behaves as a constant. Exam relevance: Complex Analysis (specifically Analytic Functions) carries around 30-35 marks in CSIR NET and appears as a high-weightage topic in Unit 2 of mathematical sciences. Most students lose marks here because they fail to distinguish between local differentiability and global analyticity, or they get bogged down in long-form differentiation instead of applying Milne-Thomson directly. Watch till the end for the shortcut. ━━━━━━━━━━━━━━━━━━━━━━ FREE RESOURCES ━━━━━━━━━━━━━━━━━━━━━━ Join our What’s app community for free notes, PYQs & exam updates: [https://chat.whatsapp.com/Cld3F8Mri1o...](https://www.google.com/search?q=https...) ALPHA STRIKE Test Series (18 mocks — CSIR NET & MH-SET)only at ₹499 [https://nextgenalphamaths.com/courses...]() ━━━━━━━━━━━━━━━━━━━━━━ ABOUT NGAM ━━━━━━━━━━━━━━━━━━━━━━ Next Gen Alpha Mathematics | Free CSIR NET & GATE Maths lectures Faculty: Rohit Sir (CSIR JRF, GATE) & Abhishek Sir (CSIR JRF, GATE) Website: [https://nextgenalphamaths.com]() Instagram: [  / nextgenalpha.mathematics  ]() [   • Master Analytic Functions in 1 Hour!| CSIR...  ]()