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.
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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