First Course on PDEs - I | NPTEL | Prof. Datti & Prof. Nandakumaran | Syllabus & Details
Course Details
| Exam Registration | 88 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 8 weeks |
| Categories | Mathematics |
| Credit Points | 2 |
| Level | Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 13 Mar 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 16 Feb 2026 |
| Exam Date | 28 Mar 2026 IST |
| NCrF Level | 4.5 — 8.0 |
First Course on Partial Differential Equations - I: A Foundational Journey
Partial Differential Equations (PDEs) are the cornerstone of modeling continuous phenomena in science and engineering, describing everything from heat diffusion and wave propagation to financial markets and quantum mechanics. For postgraduate students and professionals seeking a rigorous introduction, the First Course on Partial Differential Equations - I offers an unparalleled opportunity to learn from distinguished experts in the field.
Course Overview and Distinguished Instructors
This 8-week course is designed as the first part of a comprehensive semester-long curriculum, equivalent to 20 lecture hours. It is meticulously structured to build a strong theoretical foundation.
The instruction is led by two eminent professors:
- Prof. P.S. Datti: A former faculty member at the prestigious TIFR-CAM (Tata Institute of Fundamental Research - Centre for Applicable Mathematics), Bangalore, bringing deep research insights.
- Prof. A.K. Nandakumaran: A Professor at the Department of Mathematics, Indian Institute of Science (IISc), Bangalore, known for his clarity in teaching and significant contributions to the field.
This collaboration ensures a blend of profound theoretical knowledge and practical pedagogical excellence.
Who Should Enroll?
This course is ideally suited for:
- Postgraduate students in Mathematics, Physics, and Engineering.
- Researchers and professionals in scientific computing and modeling.
- Any learner with a solid background looking to formalize their understanding of PDEs.
Prerequisites
To successfully follow this course, a firm grasp of the following subjects is essential:
- Multi-variable Calculus
- Linear Algebra
- Ordinary Differential Equations
Detailed 8-Week Course Layout
The syllabus is carefully sequenced to progress from fundamental concepts to classical equations of mathematical physics.
| Week | Topics Covered |
|---|---|
| Week 1 | Introduction, Preliminaries |
| Week 2 | First Order Equations – Method of Characteristics |
| Week 3 | First Order Equations – Multi-variables and Classification |
| Week 4 | Laplace and Poisson Equations |
| Week 5 | Laplace and Poisson Equations (Continued) |
| Week 6 | 1D Heat Equation |
| Week 7 | 1D Wave Equation |
| Week 8 | 1D Wave Equation (Continued) |
Recommended Textbooks and Resources
The course draws from a rich set of literature, including the instructors' own authoritative text:
- Primary Text: A. K. Nandakumaran and P. S. Datti, Partial Differential Equations: Classical Theory with a Modern Touch, Cambridge University Press (2020). This book, part of the Cambridge-IISc Series, is the recommended core text and is expected to be available from April 2020.
- Supplementary References:
- L. C. Evans, Partial Differential Equations, AMS (1998).
- Fritz John, Partial Differential Equations, Springer-Verlag, Third Edition (1978).
- R. C. McOwen, Partial Differential Equations – Methods and Applications, Pearson Education, Second Edition (2005).
- A. K. Nandakumaran, P. S. Datti and Raju K George, Ordinary Differential Equations – Principles and Applications, Cambridge (2017).
For prerequisite refreshment, learners are encouraged to refer to the NPTEL video course on Ordinary Differential Equations.
Why Take This Course?
This course is more than just a series of lectures. It is a structured pathway to mastering the language of continuous systems. By focusing on first-order equations and the three fundamental second-order equations (Laplace, Heat, and Wave), you will gain the essential tools to analyze and interpret a vast array of physical problems. Learning from professors associated with premier institutions like IISc and TIFR ensures you are receiving education at the highest standard.
Course Start Date: January 2021
Duration: 8 Weeks
Level: Postgraduate
Prepare to delve into the fascinating world of Partial Differential Equations and unlock the mathematics behind the physical world. This first course is your critical first step.
Enroll Now →