MTH 452- 552 : NUMERICAL ODEs - Winter 2018
General information
General information
Instructor: Malgorzata Peszynska (Contact information including office hours is on Instructor's website.) See also instructor's department website.

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 C1 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!