Ordinary & Partial Differential Equations Course | NPTEL IIT Roorkee
Course Details
| Exam Registration | 78 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Language of Change: A Deep Dive into Differential Equations
Differential Equations form the cornerstone of mathematical modeling for dynamic systems. From predicting the trajectory of a satellite to simulating the flow of heat in an engine, they are indispensable in engineering and scientific discovery. If you've ever wanted to master this powerful language of change, a remarkable opportunity awaits you.
The National Programme on Technology Enhanced Learning (NPTEL) offers a comprehensive course titled "Ordinary and Partial Differential Equations and Applications", delivered by distinguished professors from the prestigious Indian Institute of Technology (IIT) Roorkee. This 12-week journey is designed to transform your understanding from fundamental concepts to advanced applications.
Meet Your Expert Instructors from IIT Roorkee
The course is led by two eminent faculty members whose expertise and teaching excellence ensure a rich learning experience.
Prof. P. N. Agrawal is a Professor in the Department of Mathematics at IIT Roorkee. With a research focus on Approximation Theory and Complex Analysis, he brings decades of academic rigor. Prof. Agrawal is a seasoned NPTEL educator, having delivered 13 video lectures in Phase I and contributed to pedagogy projects. He has supervised nine Ph.D. theses and has an impressive publication record of over 187 research papers. His experience in teaching courses like "Integral Equations and Calculus of Variations" ensures clarity in delivering complex topics.
Prof. D. N. Pandey is an Associate Professor in the same department. An expert in semigroup theory and functional differential equations, Prof. Pandey has a wealth of experience from institutions like BITS-Pilani and LNMIIT Jaipur. He is the author of a published book on nonlocal functional evolution equations and has created e-notes for UGC's e-Pathshala. Having guided multiple Ph.D. students and published over 60 research papers, he excels at bridging theoretical concepts with practical applications.
Who Should Take This Course?
This course is meticulously designed for:
- Undergraduate (UG) and Postgraduate (PG) students in Engineering (all branches).
- UG and PG students in Science (Physics, Chemistry, Mathematics).
- Researchers and professionals looking to solidify their foundational knowledge in differential equations.
- Anyone preparing for competitive exams that require a strong grasp of advanced engineering mathematics.
Course Overview: What Will You Learn?
This is a foundational course that progresses systematically from Ordinary Differential Equations (ODEs) to Partial Differential Equations (PDEs), emphasizing both theory and real-world applications in fields like control theory, numerical analysis, and dynamical systems.
Detailed 12-Week Course Layout
| Week | Topics Covered |
|---|---|
| Week 1 | Existence and Uniqueness of Solutions of ODE |
| Week 2 | Linear Systems of Differential Equations |
| Week 3 | Power Series Solutions for ODEs |
| Week 4 | Frobenius Method for Series Solutions |
| Week 5 | Stability of Systems, Autonomous Systems, Phase Plane Analysis |
| Week 6 | Boundary Value Problems, Green's Function |
| Week 7 | Introduction to First Order PDEs |
| Week 8 | Nonlinear PDEs of First Order, Charpit's Method |
| Week 9 | Classification & Canonical Forms of Second Order PDEs |
| Week 10 | Laplace Equation and Poisson Equation |
| Week 11 | Wave Equation |
| Week 12 | Heat (Diffusion) Equation, Duhamel's Principle |
Essential Reference Books
To complement the video lectures, the instructors recommend the following authoritative texts:
- Braun, M. - Differential Equations and Their Applications (Springer).
- Deo, S.G., Lakshmikantham, V., and Raghvendra, V. - Text Book of Ordinary Differential Equations (Tata McGraw Hill).
- Simmons G.F. - Ordinary Differential Equations with Applications (Tata McGraw Hill).
- Sneddon, I. N. - Elements of Partial Differential Equations (McGraw-Hill).
- Amarnath, T. - An Elementary Course in Partial Differential Equations (Narosa).
- Rao, K. S. - Introduction to Partial Differential Equations (PHI Learning).
Why Enroll in This NPTEL Course?
World-Class Instruction for Free: Learn directly from IIT Roorkee professors without any cost, accessing the same quality of education offered to IIT students.
Structured Learning Path: The 12-week module provides a clear, step-by-step progression from basics to advanced topics, ensuring a solid conceptual build-up.
Focus on Applications: The course consistently highlights the tremendous applications in diverse fields like control theory, dynamical systems, and numerical analysis, showing you the "why" behind the "what".
Flexibility: As an online course, you can learn at your own pace and convenience, making it ideal for students and working professionals alike.
Whether you are an engineering student aiming to ace your exams, a science enthusiast curious about mathematical modeling, or a professional seeking to refresh core concepts, this course on Ordinary and Partial Differential Equations is your gateway to mastering the mathematics of change. Enroll today and start your journey with the experts from IIT Roorkee.
Enroll Now →