Overview

Instructor

Jeffrey Wong ( main site)

Email

jtwong at math dot duke dot edu

Office

Physics 029B

Office Hours

M11-12, F4-5 or by appointment

Lectures

TTh 4:40-5:55 (Physics 259)

Syllabus

Available here.

Textbook

Polking, Boggess and Arnold, Elementary Differential Equations withs Boundary Value Problems, 2nd Edition.

Synopsis

First order ordinary differential equations and linear systems. Brief introduction to nonlinear dynamics in 2d and qualitative behavior. Fourier series, partial differential equations, boundary value problems and Sturm-Liouville theory.

Course Objectives

This course will introduce the classical theory of differential equations. We will begin with the fundamentals of ordinary differential equations and then build on this theory to solve some partial differential equations. While we will learn the mechanics of computing solutions, the primary goal of the course is to develop a way of thinking and an understanding of the rich structure that underlies the methods.

Prerequisites

A solid understanding of fundamentals from linear algebra is essential. This includes the concepts of linearity, span, basis, eigenvalues and eigenvectors as well as the ability to use them in argument and calculation. We will also make frequent use of single-variable and multi-variable calculus as covered in Math 212. It will be beneficial to review this material on your own; some key concepts will be briefly reviewed in class/homework.

Grading

Your grade will consist of the following components:

• Weekly homework (15%), lowest dropped
• Midterm exams (20% each)
• Final exam (45%)

Important note: Your final grade will be based on a complete evaluation of your performance in the course, which includes some instructor discretion. The percentages listed are intended to give you a sense of the relative importance of each component; consider the computed value to be a baseline and not a formula for computing your grade.

Homework

• Homework will be assigned weekly, except before midterms and the final exam. Due dates will be listed on Sakai; typically one week after assigned.
• No late homework will be accepted, barring exceptional circumstances as per Duke policy. The lowest homework score will be dropped.
• Working and studying in groups is encouraged (you will get much more out of doing homework if you discuss it with others!). However, you should write your own solutions to each problem in your own words.
• Solutions should be complete arguments; the process by which you arrive at the solution is far more important than a correct answer.
• Solutions should be clearly readable and in the order of the assigned problems.

Ethics

Students are expected to follow the Duke Community Standard. If a student is found responsible for academic dishonesty through the Office of Student Conduct, the student will receive a core of zero for that assignment. If a student’s admitted academic shonesty is resolved directly through a faculty-student resolution agreement approved by the Office of Student Conduct, the terms of that ent will dictate the grading response to the assignment at issue.