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Ordinary Differential Equations

By Prof. Kaushik Bal   |   IIT Kanpur
Learners enrolled: 715   |  Exam registration: 28
ABOUT THE COURSE:
Differential Equations are one of the central topics which results when studying models arising out of physical systems. Most often than not the nonlinear nature of the equation forces us to study the qualitative and geometric theory of equations and dynamical systems. In this course we start by first studying about the various aspect of Linear Systems and then analyze local and global behavior of nonlinear systems using techniques from Linear theory.

INTENDED AUDIENCE: Undergraduate students in Mathematics, Physics and Engineering, Graduate students in Mathematics.

PREREQUISITES: Linear Algebra and Several Variable Calculus.
Summary
Course Status : Ongoing
Course Type : Core
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 22 Jul 2024
End Date : 11 Oct 2024
Enrollment Ends : 05 Aug 2024
Exam Registration Ends : 16 Aug 2024
Exam Date : 02 Nov 2024 IST

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


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Course layout

Week 1: Review of Linear Algebra and Several Variable Calculus.

Week 2: Picard-Lindeloff Theorem for Existence and Uniqueness of Solution, Continuous Dependence on Initial Data.

Week 3: Linear System: Fundamental Existence Theorem and Uniqueness theorem, Solution Subspace, Linear Independence and Wronskian.

Week 4: Matrix Exponential: Convergence, Properties. Matrix Exponential for Diagonlizable Matrix, Fundamental Matrix, Generalized Eigenvalues, Matrix Exponential for non-Diagonlizable Matrix.

Week 5: Phase Plane Analysis: Phase Portrait, Fixed point and Linearization, Reversible System.

Week 6: Comparison Principle, Maximum Principle and Oscillation theory.

Week 7: Periodic System, Floquet theory, Hill’s equation.

Week 8: Limit Cycle: Closed Orbit, Poincare Map, Poincare-Bendixson theorem.

Week 9: Sturm-Liouville Theory for second order equations. Properties of the eigenfunctions, Spectrum of Linear Operators.

Week 10: Linearization and Stable Manifold Theorem.

Week 11: Stability in Lyapunov Sense, Lyapunov Direct Method.

Week 12: Limit Cycle and Poincare Bendixson Theorem.

Books and references

1.Differential Equations and Dynamical Systems
(Texts in Applied Mathematics, 7) 3rd
Edition Lawrence Perko
2.Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition (Studies in Nonlinearity) 2nd Edition Steven H. Strogatz

Instructor bio

Prof. Kaushik Bal

IIT Kanpur
Prof. Kaushik Bal is an Associate Professor of Mathematics and Statistics at Indian Institute of Technology, Kanpur. My area of specialization is Partial Differential Equations most specifically of the elliptic and parabolic nature.

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: 
02 November 2024 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 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 Kanpur .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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