MAT3440
The final syllabus is given here.
The best way to prepare for the exam is to go through and solve all of the weekly exercise sets. If you are able to solve (most of) these exercises then you are well-prepared for the exam!
MAT3440 overlaps partially with MAT2440, the difference being that control theory has been removed in favor of numerical methods. A list of MAT2440 exam questions is found here. Relevant problems from earlier exams are:
MAT2440
The course MAT3440 is a continuation of MAT2440, but where control theory has been replaced by numerical methods. If you are taking the exam in MAT2440 then the syllabus is [Meiss, chapter 1-4] as well as chapter 3-4 of Terje Sund's lecture notes. A good preparation for the exam would be the exams in MAT2440 from 2010–2016.