General notes and announcements
- 19th Aug: Apart from the books mentioned in the course plan, there are a couple of other books in the library which may be of use for the course: Advanced linear algebra by Bruce Cooperstein (512.5 COO), Linear algebra by Hoffman and Kuntze (512.5 HOF), Linear algebra with applications by Gareth Williams ( 512.5 WIL).
- 19th Aug: I have corrected a crucial typographical error, pointed out by your colleague (thanks!) in tutorial 1 below, in question 4.
- 9th October: Class average for mid-sem exam is 39.7/52; maximum is 52/52.
- 15th October: There are a couple of corrections on slides 25 and 28 for ODEs, thanks to Aniket. Please take a look.
- 27th October: I have added one more slide to PDE slides, on heat equation for infinite medium/ Fourier transforms.
- 8th November: While talking with a colleague, I remembered a joke which might (or might not) be enojyable to senior engineering students. It has nothing to do with the course, but it's the cleverest joke I know on mathematical physics: Schrodinger and Heisenberg are stopped by a police officer while travelling on a German motorway. “Sir, are you aware of the speed you are travelling at?” asks the policeman to Heisenberg, who is at the wheel. “No,” comes the reply, “but I know EXACTLY where I am!” The police officer gets suspicious and asks them to open the car boot. He goes around, peeks in and shouts “Hey! Is there a DEAD CAT in here?” Schrodinger shrugs and says “there is – now.”
Handouts and slides
- Handouts for linear algebra, which is roughly the first third of the course, are available here.
- Slides for linear algebra with overlays are available here.
- Handouts for systems of ordinary differential equations, which is roughly part II of the three part course, are available here.
- Slides for systems of ODEs with overlays are available here. There are changes in slides 25 and 28, made on 15th October.
- Slides for linear PDEs with overlays are available here and handouts are available here.
- Slides for a one-off topic of Legendre equation are available here.
- Brief notes on the Bessel equation, discussed in the class on 15th November are available here. One of the errors in the discussion in the class has been corrected in the notes. To those who remember - all works well if you take your constant to be lambda^2, instead of lambda. This still doesn't include some material which we will cover on the 18th.
Homework and solutions
For feedback on homework, please seek help from the TAs, Shivajee (Mon 6pm-7pm) and Om Prakash (Tues 4pm-5pm), in the first instance. Both are in 5/343. My own office hour is Fri 2.15pm-3.15pm, till the end of September (it will change post mid-sem); I am in 6/336A.
- Homework tutorial 1.
- Solution to homework tutorial 1.
- Homework tutorial 2.
- Solution to homework tutorial 2. One typo in Q 4 corrected on 2nd September (Aniket is a star).
- Homework tutorial 3. This is revision of what has been covered before 23rd August. Update on 29th Aug - a typo in the last question has been corrected (thanks to Aniket).
- Solution to homework tutorial 3.
- Homework tutorial 4.
- Solutions to quiz 1.
- Solutions to homework tutorial 4.
- In class tutorial on Fourier series and its solutions.
- In class tutorial on eigenvalues and eigenvectors and its solutions. I don't think the point about orthonormality was discussed in the class.
- Homework tutorial 5. You can skip question 3.
- Homework tutorial 6. This contains some physical models which we haven't discussed in the class, but which are hopefully simple enough.
- Solutions to homework tutorial 5. Please try the problems first!
- Solutions to homework tutorial 6. Please try the problems first! Note - Wronskian being zero does not automatically imply linear dependence.
- Homework tutorial 7.
- Homework tutorial 8.
- Solutions to homework tutorial 7. Update on 5th November - corrected the answer to the last Q. For the first problem, it is assumed that u, v are non-negative (they are populations) in order to specify the nature of their relationship.
- Solutions to homework tutorial 8. Please try problems first!
- In-class tutorial 7 and solutions. Please try problems first!
- Homework tutorial 9.
- Solutions to homework tutorial 9.