You have a lot of latitude to assume standard results. But do state them precisely and cite a source. I want you to approach these assignments as if each question was a piece of a research paper. Write it up well, cite your sources, contribute something clear and definite (i.e. the result you are asked to show) but don't reinvent the wheel and don't get stuck on any single small issue.

The Matlab numerical examples are important. So far, they are the computational, modern component of this class. The lesson to learn is how to use computation to advance understanding, to confirm symbolic results and to provide new insights that can be the springboard for further mathematical thinking.

For each problem, what you should put in the writeup is one or two small figures, and a short explanation that makes clear how the figure was generated (at the mathematical level, not the implementation aspects) and what conclusions can be drawn from the results shown in the figure. Again, the style should be similar to what you might write in the "results" section of a research paper.