Complex Analysis | CSIR NET Mathematics | Important Questions | IFAS
In this session by IFAS, Rohit Sir conducts a "Game Changer" problem-solving session on Complex Analysis, specifically tailored for CSIR NET Mathematical Science and GATE aspirants. The lecture focuses on building a strong conceptual foundation through a series of important questions covering mapping, integration, and function properties.
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👉🏻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.....)
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🎯 Target Audience: This video is highly beneficial for students preparing for:
CSIR NET Mathematics, GATE Mathematics, MH SET Mathematics, BARC, NBHM
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👇 Watch the Full Lecture to Master These Topics:
Conformal Mappings
Argument Principle
Complex Path Integration
Singularities and Residues
Cauchy’s Residue Theorem
Properties of Entire Functions
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⏱️ Timestamps - Jump to Your Topic:
[00:39] Introduction and Session Welcome
[03:13] Conformal Mapping: Determining points where is not conformal
[11:03] Argument Principle: Integrating $f'(z)/f(z)$ for a polynomial of degree 2025
[14:38] Path Integration: Evaluating $\int_C |z|^2 dz$ over a parameterized line segment
[18:36] Singularity Analysis: Residue calculation for $e^z / (z-2)^4$
[25:08] Cauchy's Residue Theorem: Evaluation of mixed-term rational functions
[31:50] Injectivity & Constant Functions: Multi-theorem analysis (Picard, Riemann, Liouville)
[41:08] Meromorphic Functions: Truth testing for compositions and singularities
[46:15] Homework Challenge: Integrating over a Limacon curve
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Lecture Summary:
This session emphasizes advanced problem-solving techniques over rote memorization. Rohit Sir covers essential theorems like the Argument Principle and Residue Theorem while challenging students with multi-layered MSQ (Multiple Select Questions) that test the limits of entire and meromorphic function theory. The session wraps up with a complex integration homework problem and a transition to Real Analysis practice.
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