Math 310 (Ordinary Differential Equations)
Office Hours Monday, Tuesday 2:30-4:30 pm;
Thursday 9-10 am; or by appointment firstname.lastname@example.org
Lecture time MWF 1:30-2:20 pm, REN 127
Textbook Differential Equations and boundary value problems, by Edwards and Penney,
Homework (15%) Homework assignments and quizzes are the most important part of this course.
Homework will be assigned during the semester, and posted on the course webpage on weekly basis.
Selected homework problems will be graded. After an assignment has been turned in, the solution to
the problems will be posted on the course webpage. Late homework (after the solution has been posted)
will not be accepted. The lowest homework assignment score will be dropped when calculating the final course grade.
Quizzes (15%) Based on the homework assignments, 11 quizzes will be given at the beginning of the class on the dates
specified on the tentative schedule. Make-up quizzes are allowed only if you get my permission ahead of time
(limited to two make-ups per student), or have a doctors note.
The lowest quiz score will be dropped when calculating the final course grade.
Midterm Exams (20% X 2)
Two midterm examinations are scheduled on the days specified on the tentative schedule.
A make-up examination is possible only
if you get my permission before the examination, or with a doctors note.
Final Exam (30%)
Final examination is scheduled on Monday, May 6, 12:30 am2:30 pm.
Course grades are determined by: A (90.0%-100%); B (80.0%-89.9%); C (70.0%-79.9%); D (60.0%-69.9%); F (<60.0%).
Course Content Outline
1. First order equations (Chapter 1: sections 1.1 1.6)---
Slope fields and integral curves
Solution techniques for separable and linear ODEs, including initial value problems
Existence and Uniqueness
Applications and modeling
Substitution techniques and exact equations
2. Introduction to numerical approximations (Chapter 2: selection from sections 2.1 2.3; sections 2.4 2.6)---
Basic models and equilibrium solutions
3. Higher order equations (Chapter 3: sections 3.1 3.3, 3.5; selection from sections 3.4, 3.6, and 3.7)---
Linear independence/dependence of solutions, and the Wronskian
Principal of linear superposition
Solution techniques for constant coefficient linear ODEs
Methods of variation of parameters and undetermined coefficients
4. Systems of ODEs (Chapter 4: sections 4.1 4.2; chapter 5: sections 5.1 5.2)---
5. Laplace transform (Chapter 7: sections 7.1 7.3, 7.5; selection from sections 7.4 and 7.6)---
Definitions and basic properties of the Laplace transform
Definitions and basic properties of inverse transforms
Solving initial value problems, including equations with piecewise-continuous input functions
Impulses and delta functions
6. Power series (Chapter 8: sections 8.1 8.2)---
Basic properties and techniques of power series
Series solutions to an ODE at an ordinary point
The student will learn how to model a dynamic physical phenomenon as a differential equation
The student will gain mastery of standard methods for solving initial value problems, both analytically and numerically
The student will be able to analyze and interpret qualitative aspects of solutions to ODEs