Functional Analysis Course | Applications in Math & Engineering | IIT Professor
Course Details
| Exam Registration | 45 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 24 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Abstract Spaces: A Comprehensive Guide to Functional Analysis
Functional Analysis stands as one of the most elegant and powerful branches of modern mathematics, serving as the backbone for numerous advancements in science and engineering. It provides the rigorous framework needed to solve complex problems in differential equations, quantum mechanics, signal processing, and beyond. This 12-week course, meticulously designed and delivered by Prof. Akhilesh Prasad of IIT (ISM) Dhanbad, offers a unique opportunity to master both the fundamental theory and the practical applications of this vital subject.
Why Study Functional Analysis?
At its core, Functional Analysis studies infinite-dimensional vector spaces—think of spaces of functions—and the linear operators acting upon them. By abstracting the concepts of length (norm), angle (inner product), and convergence, it provides unified tools to tackle problems that are intractable with classical calculus alone. From optimizing engineering systems to formulating the principles of quantum physics, the applications are vast and profound.
Meet Your Instructor: A Renowned Expert
Learning from an authority in the field makes all the difference. Prof. Akhilesh Prasad is a Professor of Mathematical Analysis at IIT (ISM) Dhanbad with a distinguished research career.
- Research Expertise: His work focuses on pseudo-differential operators, wavelet theory, harmonic analysis, and their intersections with PDEs and mathematical physics.
- Proven Track Record: Author of approximately 100 papers in reputed SCIE journals.
- Leadership: Has successfully led 7 externally funded projects from premier agencies like DST, SERB, and CSIR.
- Mentorship: Has guided 18 research students to completion, ensuring his teaching is informed by direct supervisory experience.
This course is infused with insights from his cutting-edge research, connecting abstract theorems to novel applications in engineering and sciences.
Course Overview: What You Will Learn
This carefully structured 12-week program is designed to build your understanding from the ground up, making it suitable for dedicated undergraduate and postgraduate students.
Detailed Course Layout
| Week | Topics Covered |
|---|---|
| Week 1-2 | Foundation: Vector spaces, metric spaces, norms, and the crucial concepts of convergence and completeness. |
| Week 3-4 | Banach Spaces: Study of complete normed spaces, bounded linear operators, functionals, and dual spaces. |
| Week 5-7 | Hilbert Spaces: Inner product spaces, orthogonality, Bessel's inequality, and the foundational Riesz Representation Theorem. |
| Week 8-9 | Operators on Hilbert Spaces: Deep dive into adjoint, self-adjoint, normal, positive, and unitary operators. |
| Week 10-12 | Fundamental Theorems & Applications: Hahn-Banach Theorem, Uniform Boundedness Principle, Open Mapping Theorem, and their powerful applications to classical analysis. |
Who Should Enroll?
- Intended Audience: Undergraduate and Postgraduate students in Mathematics, Physics, Statistics, and related engineering fields.
- Prerequisites: A solid grasp of basic linear algebra and real analysis (as available on the NPTEL portal) is desirable to fully engage with the material.
- Industry Support: This is not just pure mathematics. Functional Analysis is a core requirement with significant applications in Quantum Mechanics, Signal Processing, Control Theory, Differential Equations, and Numerical Analysis. The abstract tools you learn here directly solve concrete problems in science and technology.
Essential Learning Resources
To complement the lectures, the course recommends several classic texts that have guided generations of mathematicians:
- Bachman & Narici: Functional Analysis – A clear and accessible introduction.
- Erwin Kreyszig: Introductory Functional Analysis with Applications – Renowned for bridging theory and practice.
- B. V. Limaye: Functional Analysis – A comprehensive text popular in the Indian academic context.
- Walter Rudin: Functional Analysis – A concise and rigorous masterpiece for deep theoretical understanding.
Conclusion: Your Gateway to Advanced Mathematics
This course on Functional Analysis is more than a series of lectures; it's a guided journey into the language of modern applied mathematics. Under the expert guidance of Prof. Akhilesh Prasad, you will not only learn to prove abstract theorems but also develop the ability to see how these theorems empower innovation across scientific disciplines. Whether you aim for advanced academic research or a career in cutting-edge technology, mastering Functional Analysis is a transformative step. Enroll today and begin building the sophisticated mathematical intuition that will define your future work.
Enroll Now →