Saturday, 23 April 2016

Coordinate systems for calculus of variations

Your class rep wrote me "A student asked me about calculus of variations, if we have to be able to define coordinate systems ourselves? For example in Problem sheet 8 Question 8, students might struggle to get started on it."

This question addresses a common type of anxiety that some of you may feel. It is unjustified.

Problem sheet exercises are not necessarily model exam questions. When I list question 8 as "important" this means that I think it is important you understand how this problem is solved, and that it is a good exercise. Of course, in this question a "tricky" part is how to define the coordinates. If I would use this example as the base for an exam question, I would find it most important that you can show how to apply the Euler Lagrange equation. Most likely, as getting the coordinates right is perhaps a little tricky, I would most likely suggest you to use certain coordinates, since without a reasonable choice, you would not be able to get anywhere.

As I told many of you before: it is my "problem" to set an exam that tests how well you understand the material. So I would aim to avoid exam questions to depend on "tricky" bits that are not at the core of the course material.

So in answer to the question whether "[do] we have to be able to define coordinate systems ourselves?", the answer is "I would likely avoid obstacles, so if the choice of coordinates is not obvious, I would likely provide you with a suggestion."

I hope this helps.

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