In this honors seminar, we will explore the subject of ordinary differential equations (ODEs). We will focus on the behavior of solutions and their applications, with a large collection of examples using the textbook Exploring ODEs (Trefethen, Birkisson, Driscoll). We will only briefly discuss numerical methods, but will rely on MATLAB and Chebfun for illustration. Our goal is to develop a qualitative understanding of initial-value, boundary-value, and eigenvalue problems as they occur in practice in problems of science, engineering and medicine.

#### Prerequisites

Calculus I,II,III and Linear Algebra, or permission of the instructor. Familiarity with at least one programming language is strongly recommended. The language used in the course will be MATLAB, but prior experience with MATLAB is not required.#### Textbook

The course textbook is Exploring ODEs by L. N. Trefethen, A. Birkisson and T. A. Driscoll.#### Assignments and grading

There will be 5-6 homework assignments and 1-2 course projects/presentations. You are encouraged to write up your homework and submit in PDF format, generated using LaTeX, Word, etc. If you don't already know LaTeX, it is a typesetting system for producing high-quality scientific and mathematical documents, and it is worthwhile learning. The LyX word processor is an easy to use front-end for LaTeX.Grading will be based approximately 60% on homeworks and 40% on the course projects/presentations, with class participation taken into account. Please see NYU's Academic integrity policies.