Real Analysis | Lecture 5 : Riemann Integration | Assistant Professor | UPSC & UPHESC

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

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📌 Coming Next

➡ Lecture 6: Riemann Integrability Theorems & Properties

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