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Advanced Course on Partial Differential Equations - II

By Prof. A. K. Nandakumaran, Prof. P.S. Datti   |   IISc Bangalore
Learners enrolled: 515   |  Exam registration: 2
ABOUT THE COURSE:
This is a continuation of our earlier NPTEL course “Advanced Course on Partial Differential Equations – I”. This course is also for 8 weeks consisting of 20 one hour lecture hours. Half of the course (roughly 10 hours) is devoted to various aspects of elliptic equations and the rest deals with evolution equations (using the semi-groups as the tool).

INTENDED AUDIENCE: Mathematics, Science and Engineering.

PREREQUISITES: Measure and , Integration; Functional Analysis, including Semi-group theory. Basic PDE. NPTEL Course on “Advanced Course on Partial Differential Equations – I”
Summary
Course Status : Upcoming
Course Type : Core
Language for course content : English
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Postgraduate
Start Date : 17 Feb 2025
End Date : 11 Apr 2025
Enrollment Ends : 17 Feb 2025
Exam Registration Ends : 24 Feb 2025
Exam Date : 03 May 2025 IST

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


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Course layout

Week 1:  Elliptic equations: Weak (Generalized) solutions of boundary value problems. Existence and Uniqueness results

Week 2: Eigenvalues and eigenfunctions. Variational properties – Rayleigh-Ritz quotient

Week 3: 
Asymptotic behavior of eigenvalues. Non-homogeneous boundary values

Week 4: 
Regularity results. Smoothness of weak solutions

Week 5: 
Evolution equations. Abstract formulation. Semi-group theory. Hille-Yosida theorem (Only statements of the main results)

Week 6: 
Parabolic and Hyperbolic equations

Week 7: 
Schrodinger equation

Week 8: 
Perturbation results. Schrodinger equation with a potential.

Books and references

1. S. Kesavan, Topics in Functional Analysis and Applications
2. Robert S. Strichartz, A guide to Distribution Theory and Fourier Transforms, World Scientific (1994)
3. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer (2011)
4. Robert A. Adams and John J. F. Fournier, Sobolev Spaces (2008)
5. L. C. Evans, Partial Differential Equations, AMS (1998)
6. R. C. McOwen, Partial Differential Equations – Method and Applications, Pearson Education, second Edition (2005)
7. A. K. Nandakumaran and P. S. Datti, Partial Differential Equations-Classical Theory with a Modern Touch, Cambridge (2020) (Cambridge-IISc Series), Also see, NPTEL Video course(2020), https://nptel.ac.in/courses/111108144 and https://nptel.ac.in/courses/111108152
8. 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
A.K. Nandakumaran is a Professor at the Department of Mathematics, Indian Institute of Science, Bangalore.


Prof. P.S. Datti

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: May 3, 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


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