Section H.6 The 2021 exam
Like the The 2022 exam, this is an open book exam written by myself. Compared with this year, there is a small difference in notation when talking about ‘higher order functions’: While this year in Convention 1.58 we agreed to write things like \(\Phi(c)(b)\text{,}\) in that year we sometimes wrote things like \((\Phi(c))(b)\) with an extra set of brackets for emphasis. Feedback from students (after the unit was over) was that they found the \(\Phi(c)(b)\) notation less confusing.
Another small notational thing to be aware of is that in previous years we wrote \(L^2(a,b)\) rather than \(L^2([a,b])\text{.}\)
As with the The 2022 exam, if I were repurposing this as a closed book exam, I would replace some of the earlier parts of questions with questions asking you to recall various definitions and results from lectures.
Finally, there appears to be a typo in the solutions to Question 3(c)(ii): the second and third occurrences of \(C^0([-1,1])\) should be replaced with \(S\text{.}\)
