Math 310 (Ordinary Differential Equations)
Office Hours Monday 9:30-11:00am, Thursday 1:00-3:00pm; or by email appoitment email@example.com
Lecture time MWF 11:30am-12:20 pm, MCCL 209
Textbook Differential Equations and boundary value problems, by Edwards and Penney,
Homework (20%) Homework assignments and quizzes are the most important part of this course.
Homework will be assigned during the semester 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.
Homework is due at the beginning of the class on the due date. Each student will be given one opportunity
to hand in an assignment late for up to two days.
However, if the assignment is handed in after the solution has been posted a penalty of 20% will be applied.
Quizzes (15%) Based on the homework assignments, 10 quizzes will be given at the beginning of the class
on the dates specified on the tentative schedule. Each student will be
given two opportunities to either make-up a missed quiz or retake a bad quiz.
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 (25%)
Final examination is scheduled on Friday, December 20, 2013, 10:00 am12:00 pm. No make-up finals.
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