How to make students learn prerequisits

Throughout this year (at least some of) my students found it hard to follow the theory part of a computational physics course I thought. This was mostly because they lacked the mathematical foundations they should have learned already years ago.

Since I did not want to lower the course level to that of an introductory course in mathematics, I adjusted it only insofar that I tried hard to simplify the presentation. In addition, I offered my help in consultation hours and the possibility to discuss selected exercises in detail during the lectures if I get detailed questions (which I almost never got). Finally, I tried to design exercises in a way which should make them learn basics as well. I also announced very early that knowledge of basics will be a strict requirement for the exam. The students already have a Bachelor degree and should in principle know how to learn from books by themselves. However, many of them preferred to stay idle throughout the year and to wait for the sample solutions I slowly and reluctantly handed out. They then tried to learn those (more or less by heart) instead of learning the methods behind. This happened even though I had announced that this would not be useful, especially because they are allowed to use all written/printed resources.

Now a relatively large number (1/4-1/3) opted out (did not hand in a solution) and will repeat the exam in 2 month. This apparently means that they want to use more time to prepare themselves. Others will speculate that the next exam will be similar (since I thought the course for the first time they did not have any old sample solutions).

For at least the first group of people the declared goal of making them learn the basics might therefore be reached. However, I would like to achieve this in a less forceful way such that the lectures become more enjoyable for them. So, how can I make them start to learn the the prerequisites early? In a sense I would like to change their general strategy to wait until the end and to solve the problem of completing the exam by learning by heart.

The problem is complicated a bit by the fact that the audience is mixed from different fields with different degrees.

The obvious solution to improve the teaching of their early math courses is unfortunately not something I can provide without a general strategy change by the University. Obviously I will always try to improve the quality of my own teaching but I do not want to reduce the level of the course to zero. My course already included a brief repetition of required basics.