Power series solutions, including Bessel functions. The Laplace transform. Linear systems of differential equations. Qualitative properties and existence of solutions. The basic content of the course is fundamental for any student wanting to learn about classical applications of mathematics in physics and engineering.
Physical phenomena are almost without exception modeled by differential equations.
Also, the course introduces students to ideas which permeate higher mathematics, such as linear independence, existence of solutions, etc. The anticipated class size is between ten and fifteen. Class time will be taken up by lectures, dialogue, discussion of problems and exercises, and presentation of examples in a mix determined by the instructor. There may be some small group work, particularly doing examples once guiding principles have been provided. Class participation is important.