MA 207 - Differential Equations II, Autumn 2016-17

Instructor Name Swapneel Mahajan

Course Type Core for EP students (Half-sem)

Course overview

Power series method of solving linear ODEs. Frobenius method for regular singular points.

Legendre equation and its solutions, Legendre Polynomials. Bessel equation, Bessel functions, Bessel expansion theorem. Fourier series and their properties, application of fourier series in solving 1-D heat and wave equations (with various boundary conditions).

2-D wave equation (square and circular domain) and visualisation of modes. Application of Bessel functions of the first and second kind.

Laplace equation, and variable separation techniques to solve it.

Prerequisites

No formal prerequisites. However knowledge of MA 108, and MA 205 might be helpful.

Credit distribution

There was one quiz (30%) and one end-sem (70%), both MCQ.

Feedback on Lectures

Slides were used for the entire course. A separate set of lecture notes for the entire course was uploaded on the course website the very first day. These lecture notes complement the slides and are a better reading material for a thorough understanding. Classes were pretty engaging and quite enjoyable.

Feedback on tutorials, assignments and exams

Tutorials were instrumental to the understanding of the course. Exams were completely MCQ based. Model papers were given to get a feel for the question paper. Solutions are put up immediately after the paper. Grading was fair.

Relevant References

The following books can be used as references to complement the lecture notes, which are quite comprehensive themselves.

1. Elementary Differential Equations and Boundary Value Problems - William E. Boyce, Richard C. DiPrima
2. George F Simmons’ Differential Equations: especially for proofs of the theorems discussed in lecture notes
3. Fourier Series and Boundary Value Problems - James Brown, Ruel Churchill
4. Introduction to Differential Equations - Coddington: for Fuchs-Frobenius theory

Pro-tips

Practice the tut problems and read the lecture notes, as they’re more helpful than the lecture slides. Towards the end, the course gets a bit heavy, so devote time to solving problems on your own. Towards the end the classes also get a bit more interesting, which helps. Thorough study of the lecture notes and sufficient practice are enough to do well in this course.

Respondent Hrishikesh Iyer

Note: This is a review to help you make a more informed choice about how to study for this course and/or choosing this course. While we've tried to keep it objective and complete, one must keep in mind that students have varying interests, methods of study, and the course itself changes from year to year.