Singularity | Complex Analysis | CSIR NET Mathematics | IFAS | L3

Описание: In this lecture by IFAS, Rohit Sir explains the core concepts of Complex Analysis, focusing specifically on Singularity and Harmonic Functions. This session is a vital part of the Complex Analysis series, essential for CSIR NET Mathematical Science, GATE, and SET aspirants to build a strong conceptual foundation and improve problem-solving skills for analytic functions and their points of non-analyticity.

🔥 Join India's Best Mathematics Coaching for CSIR NET and GATE Exams - IFAS Online! STARTING SOON: Super Emotion Batch 7.0 (From 12th Jan 2026)

👉🏻IFAS CSIR UGC NET Mathematical Science Result👈🏻:
CSIR - NET June 2025 - Total Selections: 4200+ (CSIR UGC JRF AIR 1, 2, 6, 6, 10.....)
CSIR - NET Dec 2024 - Total Selections: 4000+ (CSIR UGC JRF AIR 5, 6, 6, 7, 8, 9, 10......)
CSIR - NET June 2024 - Total Selections: 2000+ (CSIR UCG JRF AIR 3, 10, 13, 15, 16.....)
CSIR - NET Dec - 2023: Total Selections: 1200+ (CSIR UGC JRF AIR 2, 4, 5, 7, 12, 15, 18, 19......)
CSIR - NET June - 2023: Total Selections: 1000+ (CSIR UGC JRF AIR 2, 6, 8, 9.....)
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
🎯 Target Audience: This video is highly beneficial for students preparing for:
CSIR NET Mathematics, GATE Mathematics, MH SET Mathematics, BARC, NBHM
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

👇 Watch the Full Lecture to Master These Topics:

Harmonic Functions
Harmonic Conjugates
Analytic Function Properties
Range of Analytic Functions
Constant Function Theorems
Singularity Definition
Types of Singularities by Example
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
⏱️ Timestamps - Jump to Your Topic:

[00:06] Introduction and Session Welcome
[02:24] Definition and Examples of Harmonic Functions
[06:47] Problem Solving: Is $\log(x^2 + y^2)$ Harmonic?
[11:59] Key Results on Analytic Functions and Harmonic Conjugates
[14:49] Practice Question: Finding $V_y$ given Harmonic $U$
[17:26] Theorem: Analytic Functions with Empty Range Interior
[22:15] Proof: Why $|f(z)| = \text{Constant}$ implies $f(z)$ is Constant
[28:32] Introduction to Singularity: Definition and Regular Sets
[29:46] Finding Singularities for $z/\sin(z)$ and $e^{1/z^2}$
[32:02] Example: Function with Uncountably Many Singularities
[37:49] Advanced Problem: Singularities of $1/(e^z + 1)$ and Topological Properties
[41:27] Conclusion and Preview of Complex Integration
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Lecture Summary:

In this session, Rohit Sir provides a bridge between basic definitions of analyticity and advanced properties of complex functions. The lecture covers everything from the verification of harmonic conjugates to the topological classification of singularity sets. A highlight of the session is the discussion on "Constant Function Theorems," where it is shown how the geometric nature of a function's range can force it to be constant. The lecture concludes with a detailed look at singularities, preparing students for complex integration and residue calculus in subsequent sessions.
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

🔗 Important Links:
🌍 Visit our Website: https://ifasonline.com
📞 Contact for Queries: 9172266888
📲 WhatsApp: https: https://whatsapp.com/channel/0029VbCV...
🔥 Qualification Prediction (Free Tool): https://ifasonline.com/QualificationP...
📘 Get Detailed Free Counselling: https://ifasonline.com/csir-net/mathe...
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Download IFAS: 👇
📲Android: https://play.google.com/store/apps/de...
📲 Ios: https://apps.apple.com/us/app/ifas/id...
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
CSIR NET Mathematical Science Live & Recorded Course –
https://ifasonline.com/csir-net/mathe...
GATE Mathematical Science Recorded Course –
https://ifasonline.com/gate/mathemati...
MH SET Mathematical Science Recorded Course –
https://ifasonline.com/mh-set/mathema....
📘 Buy CSIR NET Mathematical Science Books:
https://ifasonline.com/csir-net/mathe...
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
📞 Contact for Admission: 9172266888

Stay Updated Via Other Social Media:
✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu...
✔Instagram:   / csir_net_mathematical_science  
✔Facebook:   / ifasmaths  
✔WhatsApp: https: https://whatsapp.com/channel/0029VbCV...
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
#csirnetjune2026 #csirnetmaths #csirnetmathematics #csirnetmathematicalscience #csirnetpreparation #ifas