Revised Answer Sheet 7 + typos in lecture notes

I have posted a revised answer key for the 7th problem sheet. I have corrected some typos and added a few clarifying remarks.


Please also note a typo in the lecture notes on turning points in WKB solution:

(1) With a transformation of the form [1 + delta * z = x], you want delta = epsilon^{2/3}

(Take a look at the WKB solution to problem 7.6 and you'll see this same scaling. This is what one gets for 'typical' first-order turning points, and that's what leads to Airy's equation.)

WKB solution for problem 7.6

A WKB solution (courtesy Peter Howell) for problem 7.6 has now been posted.

Solution Set 7 posted

Solution set 7 is now posted. Note that there is a separate Maple file that goes with this solution set.

Corrected version of Solution Set 6 posted

I corrected a few typos in Solution Set 6 and posted the revised version.

Solution Set 6 posted

The solutions for problem sheet 6 are posted.

Solution Set 5 posted

I've posted solution set 5.

Corrected version of Solution Set 4 posted

I've posted a corrected version of Solution Set 4. It includes additional details on various points in (for example) problems 2 and 3.

Steepest Descents

As I warned everybody in class, the method of steepesct descents can be kind of tricky. It's one of the hallmark ideas of this class because it generalizes both Laplace's method and stationary phase.

Here is an example posted online that might help.

The book by Bender & Orszag has many other steepest decents examples and I strongly encourage that you study them. (In fact, I strongly encourage that you purchase this book because you'll be referring to it many times in your mathematical career.)

If there is time, I'll try to present another example of steepest descents in lecture before the end of the term. As all of you know, we are very much restricted by the limited time we have.

Solution Set 4 posted

I've posted the solution set for the 4th problem sheet. The link is on the left.

Solution Set 3 posted

I've posted the solution set to the third problem set. (And I even remembered to do it on Wednesday night this time... Go me!)

Recruiting D. Phil students for Fall 2008

I am recruiting D. Phil students to begin during the 2008-09 academic year.

I am hoping that some of you in this class will be interested in staying in Oxford for postgraduate studies, so please contact me if you might be interested in working with me. (Then we can meet to discuss your research interests.)

To get an idea of my research, please take a look at my web page.

Solution Set 2 posted

Solution set 2 is now posted.

Update (10/26/07): I have corrected typos in the solution set.

Mathematical Contest in Modeling

I am recruiting Oxford undergraduates to form teams for the Mathematical Contest in Modeling, which is an exciting and educational opportunity.

If you want to see what applied mathematics is really like, this is a superb way to do it.

Only undergraduates are eligible, so if you or anybody you know is interested (they do not have to be a mathematics major), please let me know. Either respond here or drop me a line.

The contest occurs in the middle of February, but I'd like to assemble a team or two earlier than then if possible (teams consist of 3 people), so I hope that some of you will be interested in this.

Problem set links fixed

I fixed all the links to the problem sets and have checked all of them (and the link to the first solution set). You can now safely download the assignments from this web page.

Class assignments are posted

I've just allocated class assignments. Almost everybody got their first choice, and a couple of people got their second choice (I don't think anybody got their third choice). Classes will meet starting in week 2.

Check where you ended up and let me know if anything needs to be adjusted.

Remember that the first problem sheet should be submitted (by 4th year students only, not by the Masters students) to your TA's mailbox for this course in the basement of the Math Institute.

Masters students are free to attend sections if you want, but you shouldn't turn anything in.

Problem Sets

All of the problem sets for the term have been posted. Note that the 7th one is longer than usual, so you should budget your time so that you can spend longer on it.

4th year students: To ensure that your first problem set is marked in time for the first class section, you should submit your materials to the appropriate TA's box by Tuesday at 5pm. I realize there is less time in the first week as all of us get into the swing of things, so you can also submit it later than that to get the first and second problem sets marked at the same time. After the lecture is split into classes, I will announce due dates for problem sets 2 and onward.

Welcome to perturbation methods

This is the website for Maths C6.3 (Perturbation Methods) for the Michaelmas 2007 term.

The lecture meets on Thursdays and Fridays at 11:00 am in lecture hall 1 in the Mathematical Institute (main building). The plan is to start lectures at 11:05 and finish them at 11:55.

On this blog, I'll be posting links, answering questions that are of general relevance to the course, etc.


The classes (which meet starting in week 2) are as follows:

(1) Thursday 9:00 - 10:00 am, DHSR3 (Dartington, lecture hall 3), Teacher: Peter Howell, TA: Tim Squires

(2) Friday 1:00 - 2:00 pm, Math Inst L2, Teacher: Mason Porter, TA: David Hewett

(3) Friday 2:00 - 3:00 pm, Math Inst L2, Teacher: Mason Porter, TA: David Hewett