Real Analysis (Riemann & Improper Integrals, Sequence & Series of Functions)** This course in **Real Analysis** is designed to give you a strong foundation in two of the most important areas of higher mathematics: 1. **Riemann & Improper Integrals** – Understanding integrability, convergence tests, and applications. 2. **Sequences & Series of Functions** – Covering pointwise and uniform convergence, power series, and Fourier series. These topics are not only central to **Mathematics Honours (B.Sc./M.Sc.) courses** in universities but are also **highly important for competitive exams** like: * **IIT JAM (Mathematics & Mathematical Statistics)** – Core concepts of Riemann integration and uniform convergence frequently appear in problem-solving. * **GATE (Mathematics)** – Questions often test convergence of improper integrals and series of functions. * **CSIR NET / UGC NET (Mathematical Sciences)** – Deep understanding of convergence, continuity, and integrability is essential for tackling advanced problems. 👉 **What You’ll Gain from This Course:** * A rigorous but simple explanation of **Riemann & Improper Integrals**. * Clear understanding of **pointwise vs. uniform convergence** with solved examples. * Ability to handle **limit–integral–derivative interchange problems**. * Preparation for **university exams + competitive exams (IIT JAM, GATE, CSIR NET)**. By the end of the course, you’ll be fully equipped with the theoretical understanding and problem-solving skills needed for both **academic success** and **competitive exam performance**.