AcademicsDifferential Equations

Instructor: Matt Ollis, Sci 218, matt@marlboro.edu

Timetable: TuF 1:30 - 2:50 Sci 217

Course Description: In the sciences we often want to create a mathematical model of a process. We want this model to agree with our observations of the process and to be able to predict future behaviour. If the process we are modelling involves change over time, then our model will almost always need to consider the rate of change - so we need derivatives. Typically our model will be an equation involving derivatives; a differential equation.

In this course we study how to solve differential equations, along with many of their applications. We study exact solutions where possible and power series and numerical solutions where not. The applications will come principally from mechanics and population dynamics, but there will be plenty of others too.

The text for the course is Elementary Differential Equations by Boyce and Di Prima (7th or 8th ed.)

Grades: Your grade will be calculated as follows: Final exam 40%, homeworks 40% and quizzes 20%. Class participation and prompt submission of homework are expected. Your overall grade may move up or down a small amount due to these factors.

Homeworks: Homeworks will take two forms. You will be expected to attempt regular routine exercises from the text to make sure you stay on top of basic techniques, and to use the students' solution guide (on reserve in the library) to assess how you have done. Also, at the end of each of the six sections (see below) there will be a substantial set of questions to be handed in for marking.

Office hours: TBA

Tutoring: Julie Shumway (jshumway@marlboro.edu)

Syllabus Outline. The following is an outline of the theoretical aspects of the course. Alongside this there will be applications dropped in, both from Elementary Differential Equations and other sources.

1. Introduction: Sections 1.1 - 1.4

2. Calculus Review: Handout

3. First Order ODEs: Sections 2.1 - 2.5

4. Second Order ODEs: Sections 3.1 - 3.6

5. Power Series Solutions: Handout, Sections 5.1 - 5.4

6. Numerical Methods: Sections 2.7 and 8.1 - 8.3