Partial Differential Equations Advanced MATH 2965

[Imran]

For those interested in maths, this is a must and is available 2nd semester of 2nd year. To get ahead I would advice you to download the lecture notes and tutorial problems/solutions from online as well as the past papers that are available now. After a while they will not be available(this is my experience from 2nd year).

Furthermore, you willl find th tutorial questions are much better than any textbook, although there was a textbook that was very helpful to me-given to me by a brother at uni-most of the tute q are based on that textbook but the answers (worked ansewrs) are not available in complete detail.

So what does this subject entail?

This is basically an applied course looking at your manipulation skills rather than remembering tons of proofs etc like in real and complex analysis and in the exam you are fair game-meaning they can ask you stuff from outside the very broad "syllabus" and you are expected to extrapolate from your given knowledge to extend it to higher order problems. The lecturer is David Galloway and he is quite good except for the fact you cannot simply just swallow what he says/writes because sometimes he makes careless errors etc-other than that he's really good as well.

The assignments are also based on questions from the textbook (habermann it was I think) and having solutions to the textbook will help if you can get your hands on it-most textbooks have a worked solutions book go with it

[Imran]

You must be good with your intergal calculus from first year and be very good with manipulating differential equations(from advanced first year intergal calc). Double fourier transforms are frequently used and triple may also be asked via them providing you with a small amount of background information and making you use that given information to solve given problems-it is a bit like the very early 4u papers which would examine things covered in more detail in uni eg power series in which you are given some background and expected to use that to progress.

Your idea of limits etc and physical understanding of multiple integrals must also be strong which is where your assumed knowledge from 2nd year vector calculus and linear algebra comes in. Knowledge of physics also helps as waves are dealt with in detail and certain physical models in which you must interpret your results in the context of the question.

[Imran]

In terms of te questiosn asked in assignments and exams-historcially relevant functions etc such as the Airy function are frequently asked-usually for derivation-it would help to look at how such equations are derived as it would give you an idea of how to approaach any questions related to such equations

[Imran]

use google to get extra notes as well as other university lecture notes are available as well as exam papers which would be good preparation

[Imran]

For preparation in any maths subject before you go on to do lots of questions as people will tell you to do, it is important to build a firm base-start by doing the questions covered in the lectures again-you have worked solutions for those and make sure you write out the solution in more detail than the lecture notes if you can-this will help with obtaining a greater understanding and assessing any regions where you are weak

[Imran]

being able to manipulate Power series etc and other series is also helpful as fourier series is investigated to a small extent(Real and complex analysis is useful in this case). Vector calculus is particularly important in laplace equations where understanding physical extensions is important.

One problem u will face is that very few past exams are available, unlike a lot of the other maths. Questions are extremely long however-in the exam if you make one mistake then you are pretty much dead and buried for that question. U must have speed and be good with algerbaic manipulation. However the scaling is very good and the risk is worth it-even if u stuff one question it is not necessarily the end. There are so many questions and many that people don't have time to do as long as u use ur time wisely u can scrape in decent marks.

[Imran]

The textbook by haberman is hard to come by in the libraries, there should be a copy in the musallla soon (thanx to a brother who did the subject previously-he was a lot of help to me as well may allah reward him). It has a cover with korean written on the front but don't be taken in by that, look inside to make sure.

The solutions for that textbook are found on the useful links thread-with a lot of assignment questions u may find they are actually variations of the haberman textbook questions so the solutions were pretty helpful in answering the questions quickly