One Fine Conformal Transformation

It’s been a while since I posted a cute physics problem, so try this one for size. It is taken from a book of examples I was given in 1984 to illustrate a course on Physical Applications of Complex Variables I took during the a 4-week course I took in Long Vacation immediately prior to my third year as an undergraduate at Cambridge.  Students intending to specialise in Theoretical Physics in Part II of the Natural Sciences Tripos (as I was) had to do this course, which lasted about 10 days and was followed by a pretty tough test. Those who failed the test had to switch to Experimental Physics, and spend the rest of the summer programme doing laboratory work, while those who passed it carried on with further theoretical courses for the rest of the Long Vacation programme. I managed to get through, to find that what followed wasn’t anywhere near as tough as the first bit. I inferred that Physical Applications of Complex Variables was primarily there in order to separate the wheat from the chaff. It’s always been an issue with Theoretical Physics courses that they attract two sorts of student: one that likes mathematical work and really wants to do theory, and another that hates experimental physics slightly more than he/she hates everything else. This course, and especially the test after it, was intended to minimize the number of the second type getting into Part II Theoretical Physics.

Another piece of information that readers might find interesting is that the lecturer for Physical Applications of Complex Variables was a young Mark Birkinshaw, now William P. Coldrick Professor of Cosmology and Astrophysics at the University of Bristol.

As it happens, this term I have been teaching a module on Theoretical Physics to second-year undergraduates at the University of Sussex. This covers many of the topics I studied at Cambridge in the second year, including the calculus of variations, relativistic electrodynamics, Green’s functions and, of course, complex functions. In fact I’ve used some of the notes I took as an undergraduate, and have kept all these years, to prepare material for my own lectures. I am pretty adamant therefore that the academic level at which we’re teaching this material now is no lower than it was thirty years ago.

Anyway, here’s a typically eccentric problem from the workbook, from a set of problems chosen to illustrate applications of conformal transformations (which I’ve just finished teaching this term). See how you get on with it. The first correct answer submitted through the comments box gets a round of applaud.

conformal transformation

 

4 Responses to “One Fine Conformal Transformation”

  1. Phillip Helbig Says:

    “Those who failed the test had to switch to Experimental Physics, and spend the rest of the summer programme doing laboratory work, while those who passed it carried on with further theoretical courses for the rest of the Long Vacation programme.”

    Reminds me of the punishment for fornication, as remembered in an English folk ballad:

    If he be a married man
    Then hanged he shall be,
    And if he be a single man
    He shall marry thee.

  2. Themos Tsikas Says:

    100*sqrt(X^2-1)

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: