Course Description: This course is an introduction to differential equations for students who have studied linear algebra. You will learn about exact and approximate techniques for solving differential equations, as well as methods for predicting the qualitative behavior of the solutions. We will prove theorems about the existence and uniqueness of solutions. Throughout the course, we will consider applications to physical problems. I will give proofs in class, and the homework will contain computational as well as more conceptually oriented problems. Contents: First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability.
Prerequisites: Math 215 or 285, and Math 217.
Textbook: Boyce and DiPrima. Elementary Differential Equations, Sixth Edition. Wiley, 1997.
Course Work: There will be weekly homework assignments. We will
have two in-class midterms and a final exam. The final exam is
scheduled for Tuesday,
Grading: Grades will be based on the exams and homework. Performance in class may be taken into account. Each midterm counts 20%, the final 35%, and the homework 25%.
Office Hours: To be announced. My office is
Course Homepage: Updated information, homework sets, any handouts, etc., will be available from http://www.mathstat.dal.ca/~selinger/courses/316W00/