Ordinary and Partial Differential Equations and Applications

By Prof. P. N. Agarwal, Prof. D. N. Pandey   |   IIT Roorkee
Learners enrolled: 1104
About the course:
This course is a basic course offered to UG/PG students of Engineering/Science background. It contains existence and uniqueness of solutions of an ODE, homogeneous and non-homogeneous linear systems of differential equations, power series solution of second order homogeneous differential equations. Frobenius method, boundary value problems for second order ODE, Greens function, autonomous systems, phase plane, critical points and stability for linear and non-linear systems, eigen value problems, Sturm-Liouville problem. Classification of first order PDE, existence and uniqueness of solutions, Nonlinear PDE of first order, Cauchy method of characteristics, Charpits method, PDE with variable coefficients, canonical forms, characteristic curves, Laplace equation, Poisson equation, wave equation, homogeneous and nonhomogeneous diffusion equation, Duhamels principle. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, numerical analysis and dynamical systems etc.

INTENDED AUDIENCE : UG and PG students of technical institutions/  universities/colleges.
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Enrollment Ends : 06 Feb 2023
Exam Registration Ends : 17 Mar 2023
Exam Date : 29 Apr 2023 IST

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

Page Visits

Course layout

Week 1 :  Existence and uniqueness of solutions of ODE
Week 2 :  Linear system
Week 3   : Power Series solution
Week 4  :  Fronius  Series solution
Week 5  :  Stability of systems
Week 6  :  Boundary Value Problems
Week 7  : Introduction to First order PDE
Week 8  :  Nonlinear PDE of 1st Order
Week 9  : Classification and Canonical forms of Second order PDE
Week 10 :  Laplace  equation
Week 11 :  Wave equation 
Week 12 : Heat equation

Books and references

1. Braun, M. Differential Equations and Their  Applications, 4th Ed., Springer 2011. 
2. Deo, S.G., Lakshmikantham, V., and Raghvendra, V.,"Text Book of Ordinary Differential Equations, 2nd Ed., Tata McGraw Hill 2010. 3. Simmons G.F.,Ordinary Differential Equations with Applications, Tata McGraw Hill 2003.  
4. Sneddon, I. N., "Elements of Partial Differential Equations", McGraw-Hill Book Company 1988. 
5. Amarnath, T., "An Elementary Course in Partial Differential Equations", Narosa Publishing House (II Edition) 2012.
6. Rao, K. S., "Introduction to Partial Differential Equations", PHI Learning Pvt. Ltd. (2nd Edition) 2012.'

Instructor bio

Prof. P. N. Agarwal

IIT Roorkee
Dr. P. N. Agarwal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Gupta of the same department. He taught the course on “Integral equations and calculus of variations” several times to MSc (Industrial Mathematics and Informatics) students. He has supervised nine Ph.D. theses and has published more than 187 research papers in reputed international journals of the world. Currently, he is supervising eight research students.

Prof. D. N. Pandey

Dr. D. N. Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. Before joining IIT Roorkee, he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. His area of expertise includes semigroup theory and functional differential equations of fractional and integral orders. He has already prepared e-notes for the course titled “Ordinary Differential Equations and Special Functions” under e-Pathshala funded by UGC. Also, he has published a book titled “Nonlocal Functional Evolution Equations: Integral and fractional orders, LAP LAMBERT Academic Publishing AG Germany”. He has delivered several invited talks at reputed institutions in India and abroad. He has guided three PhD theses and has published more than 60 papers in various international journals of repute. Currently, he is supervising five research students.

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: 
29 April 2023 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.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

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 IIT Roorkee.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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