Advanced Partial Differential Equations - (Part I: Distributions and Sobolev Spaces)

By Prof. A. K. Nandakumaran, Prof. P.S. Datti | IISc Bangalore

Learners enrolled: 15

ABOUT THE COURSE:

This is intended to be a first part on Advanced Partial Differential Equations, which generally requires 40 lecture hours (One semester course). So, we plan to make this course in two parts – 20 hours each. This first part is an introduction to distributions and Sobolev spaces, which are the tools for the second part. The contents of this course are not yet part of the curriculum in many our universities. Thus, we hope that this course is beneficial to many students and teachers. We plan to offer the first part starting in August 2023 and second part may be in January (August?) 2024.

INTENDED AUDIENCE: Mathematics, Science and Engineering

PREREQUISITES: Measure and Integration; Functional Analysis, Basic PDE (for example, NPTEL courses on PDE – I & II)

Summary

Course Status :	Upcoming
Course Type :	Core
Language for course content :	English
Duration :	8 weeks
Category :	Mathematics
Credit Points :	2
Level :	Postgraduate
Start Date :	21 Jul 2025
End Date :	12 Sep 2025
Enrollment Ends :	18 Aug 2025
Exam Registration Ends :	29 Aug 2025
Exam Date :	21 Sep 2025 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Some Topics in L^p Spaces

Week 2: Topics in L^p Spaces, Locally convex topological spaces and space of test functions

Week 3: Distributions and their properties

Week 4: Distributions and their properties

Week 5: Fourier Transform & Convolution

Week 6: Convolution and Introduction to Sobolev Spaces

Week 7: Sobolev Spaces: Prolongations, Density results,

Week 8: Sobolev Spaces: Extension Theorems, Trace theorem, Imbedding theorems and equivalent norms

Books and references

1. A. K. Nandakumaran and P. S. Datti, Partial Differential Equations-Classical Theory with a Modern Touch, Cambridge (2020) (Cambridge-IISc Series) Expected to be in the market in April 2020.
2. L. C. Evans, Partial Differential Equations, AMS (1998)
3. Fritz John, Partial Differential Equations, Springer-Verlag, Third Edition (1978)
4. R. C. McOwen, Partial Differential Equations – Method and Applications, Pearson Education, second Edition (2005)
5. A. K. Nandakumaran, P. S. Datti and Raju K George, Ordinary Differential Equations – Principles and Applications, Cambridge (2017) (Cambridge-IISc Series), Also see, NPTEL Video course (2014) www.nptel.ac.in/courses/111108081

Instructor bio

Prof. A. K. Nandakumaran

IISc Bangalore

Prof. A.K. Nandakumaran is a Professor at the Department of Mathematics, Indian Institute of Science, Bangalore.

Prof. P.S. Datti

Prof. P.S.Datti is a former faculty at TIFR-CAM, Bangalore.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: September 21, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team