### MA 207 – DIFFERENTIAL EQUATIONS 2

**Course offered in:**

Autumn 2020

**Instructors:**

Prof. Amiya Kumar Pani

**Course Content:**

(Lecture wise)

- Methods to solve differential equations, like airy’s equation, power series method, convergence of series
- Legendre’s polynomials, equation
- Rodrigue’s formula, singular/ordinary points
- Bessel’s function, equation
- Initial value problems, Boundary value problems, Sturm Liouville problems
- Matrix Eigen value problem, Sturm Liouville problems continued
- Periodic functions and Fourier series
- Partial differential equations
- Laplace Equation, Poisson Equation ,Uniqueness of Solution ,Heat Conduction Equation, homogenous/non homogenous PDE solving
- Fourier transforms
- Vibrating string-wave equation, Method of separation of variables ,D’Alembert’s Method

**Prerequisites:**

Core course, no prerequisites

**Feedback on Lectures:**

Lectures cover a lot of theory, which is important but will not suffice for exams. Way more dependent on problem solving and tutorial solving. The professor doesn’t teach in a very engaging manner, to say the least. It’s slightly difficult to pay attention in class, but a lot of content is covered in each class, right from the first class. Try to keep up with the course content as much as possible, otherwise it will cause a big problem towards the end of the course.

**Feedback on Tutorials, Assignments and Exams:**

Tutorials and assignments are very good and very important. If you do the tutorials properly, the exams will be quite smooth. If you do not do the tutorials or do not solve a sufficient amount of problems, the exams will be quite hard. Exams had repeated questions from the past year papers so go through those too. Try to solve tutorials completely. If that’s not possible at least try to see at least a few questions of every type, otherwise the exams will be an issue. The end semester exam was tough, but the quiz was not when we had the course.

**Difficulty:**

It’s a course which has a vast content and requires a lot of practice and time. Do not neglect this course. Its not a super difficult course but its not easy either. Tutorials are very important. Grading was not good but you can get a good grade if you practice properly enough.

**Grading Statistics:**

**Study Material and References:**

Slides were available and have all the theory required. Preferably make notes yourself too it’ll help for a quick revision as it’ll take a lot of time to go through all the slides before the exam. Tutorials are very important but you won’t need any practice other than that. You can find tutorial solutions done in the tut sessions, as well as solutions of many problems from past year tutorials, so go through them too.

**Comments:**

The best thing to do in this course is to do the tutorials and keep up with the course content regularly, as the course progresses. Do not try to do all of it at once in the end it’ll be quite difficult. A lot of formulas are used in this course so the more familiar you get with them the better. Make a formula sheet it’ll help while studying and revising.

**Takeaways from the course:**

This course tells us how to solve differential equations. It’s very important, as you’ll need to do this in most spheres of physics, maths and engineering.

Review by – Akshay Iyer (akshaygiyer@gmail.com)

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