Real Analysis | Lecture 5 : Riemann Integration | Assistant Professor | UPSC & UPHESC
Автор: Proof
Загружено: 2026-02-21
Просмотров: 20
Описание:
Welcome to Lecture 5 of the Real Analysis series on Proof.
In this lecture, we begin one of the most important topics in Real Analysis — Riemann Integration. This topic is extremely important for:
✔ Assistant Professor Mathematics Examinations
✔ UGC NET & JRF Mathematics
✔ UPSC Mathematics Optional
✔ IIT JAM & M.Sc Entrance Exams
✔ University Semester Exams
This lecture builds the foundation required to understand integrability, upper and lower sums, partitions, and the formal definition of the Riemann integral.
🎯 In Lecture 5, we cover:
✅ Motivation behind integration
✅ Partition of an interval
✅ Upper sum and lower sum
✅ Upper and lower Riemann sums
✅ Definition of Riemann integrability
✅ Geometric interpretation
✅ Examples for conceptual clarity
This is Part 1 of Riemann Integration.
📘 Lecture 6 will cover deeper results, properties, and exam-oriented problems.
🎓 Why this lecture is important?
Riemann Integration is a core topic frequently asked in:
NET/JRF proof-based questions
Assistant Professor exams
UPSC Mathematics Optional Paper I
University theory exams
Understanding these concepts will help you solve proof-based questions with confidence.
📚 Recommended for:
Students preparing for:
✔ UGC NET Mathematics
✔ CSIR NET (Mathematical Sciences)
✔ Assistant Professor Recruitment Exams
✔ UPSC Mathematics Optional
✔ GATE & IIT JAM Mathematics
✔ B.Sc / M.Sc Mathematics
🔔 Stay Connected
📌 Subscribe to Proof for structured Mathematics lectures.
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📌 Share with friends preparing for NET / UPSC / Assistant Professor exams.
📌 Coming Next
➡ Lecture 6: Riemann Integrability Theorems & Properties
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