How to prepare?/What to review?
Students will be expected to know the material on Initial Value
Problems from what is covered in
MTH 256.
If you need a refresher, consider the online
textbook
"Elementary Differential Equations" by William F. Trench
(especially Chapter 2). You may also like other Chapters in that book,
such as on the applications, and on systems. We will likely cover also
some Boundary Value problems (Chapter 11
in online
textbook by the same author including BVP).
You will also need to know enough on eigenvalues/eigenvectors of
matrices (material covered in
MTH
306
or MTH
341), such as what can be revised
in Linear Algebra text used in MTH 341.
We will also use Taylor expansions. A lot! Those not remembering how to expand f(x+h)=f(x)+..., please review.
Last but not least. For some reason, occasionally, students have difficulty with the
Lipschitz condition. The knowledge of Lipschitz constant is needed in
numerics! (More broadly, Lipschitz condition is needed for the
uniqueness of solutions in Picard's theorem, and is less restrictive
than the C^{1} condition stated in the book above). If you need examples and like
watching movies, you can search "youtube Lipschitz condition".

The movie below is not from youtube, and it is a do-it-yourself. You can do it yourself!