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Courses » Ordinary and Partial Differential Equations and Applications

Ordinary and Partial Differential Equations and Applications

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.

Important For Certification/Credit Transfer:

Weekly Assignments and Discussion Forum can be accessed ONLY by enrolling here

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Note: Content is Free!

All content including discussion forum and assignments, is free


Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.


INTENDED AUDIENCE: UG and PG students of technical institutions/  universities/colleges.

CORE/ELECTIVE: Core and Elective

UG/PG: UG and PG

PREREQUISITES: NIL

INDUSTRY SUPPORT: NIL

3164 students have enrolled already!!

ABOUT THE INSTRUCTOR:


Dr. P. N. Agrawal 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.


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, functional differential equations of fractional and integral orders. He has already prepared e-notes for 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 Ph.D. theses and has published more than 75 papers in various international journals of repute. Currently, he is supervising five research students

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

SUGGESTED READING MATERIALS:

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.'

CERTIFICATION EXAM :
  • The exam is optional for a fee.
  • Date of Exams : October 28 (Sunday)
  • Time of Exams : Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm
  • Exam for this course will be available in both morning & afternoon sessions.
  • 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.

CERTIFICATION:

  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. 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 Roorke.It will be e-verifiable at nptel.ac.in/noc.