Sunday, 15 May 2016

Picard's Theorem

One of the students has asked me: "In the past papers, the statement of the Picard Theorem is in a different form from the version given in the notes. Which one shall we use?"

There are various versions of the Picard's Theorem, which although they may be formulated with different technical details, all essentially state the same thing, i.e. that unique solutions of ODEs can be found by means of Picard iteration. If you would be asked to state "Picard's Theorem" then of course I would be happy with any correct and sensible version of this Theorem. However, note that if I would be asking you to prove a certain result, your proof should of course be related to the Theorem that you provide, or a specific version of this Theorem (from the lectures) that I would ask you to prove.

Past exam papers are useful to get an idea whether or not you are broadly well prepared for the exam. There is little point to learn answers to past exam papers by heart. Also in most cases, the provided  "model answers" are not necessarily the unique correct formulation to an answer...

In general, let me assure you that I will give generous credit to answers to exam questions that demonstrate your understanding of the material that you are asked about, rather than split hairs over whether or not you provide exactly the answer that I would have given as a model...

1 comment: