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In this lecture by IFAS, Manoj Sir explains the advanced concepts of Sequence & Series of Functions with a focus on solving complex problems for competitive exams. This session, Part 3 of the series, is essential for CSIR NET Mathematical Science June 2026 and GATE aspirants looking to master point-wise and uniform convergence. 🔥 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: Point-wise vs. Uniform Convergence Properties of Limit Functions M-Test & Mn-Test Term-by-Term Integration and Differentiation Alpha-based Convergence Problems ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ⏱️ Timestamps - Jump to Your Topic: Timestamps - Jump to Your Topic: [00:16] Session Introduction and Welcome [05:12] Example: Point-wise Limit on Interval $[0, 1)$ vs. Uniform Convergence [15:30] Deep Dive: Relationship between Continuity and Uniform Convergence [32:45] Analysis of Series of Functions using the Weierstrass M-test [01:07:32] Advanced Problem: Solving for Parameter $\alpha$ in Convergence [01:08:01] Homework Questions and Summary of Key Concepts [01:08:33] Mentorship: Joining the Study Group and Accessing Daily Practice Tests ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 👇Lecture Summary: In this eighth lecture of the Real Analysis series, Manoj Sir focuses on Sequence & Series of Functions (Part 3), bridging the gap between theoretical definitions and exam-style problems. The session covers critical topics like uniform convergence on specific intervals and the behavior of limit functions. Manoj Sir also emphasizes consistent practice, encouraging students to engage with daily tests and scholarship sections on the IFAS platform. He concludes by providing homework problems to solidify the day's learning before the next session. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔗 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 #gatemathematics #csirnetmathematics #realanalysis #csirnetmathematicalscience #csirnetpreparation #ifas