Math 310 (Ordinary Differential Equations)
Instructor: Frank Gao
Email: fuchang@uidaho.edu; Phone:
(208) 8855274; Office: Brink 322
Course Webpage: http://www.webpages.uidaho.edu/~fuchang/Math310
Lecture Time: MWF 8:309:20 am and
11:30am12:20pm at NICCOL 006; MWF 3:30pm4:20pm at TLC 022
Office Hours: Monday 9:3011:00am, Thursday 1:003:00pm; or by
appointment
Textbook: Differential Equations
and Boundary Value Problems,
by Edwards,
Penney and Calvis, 5th
edition
Homework (20%) Homework is the most important part of this
course. Homework problems will be assigned during the semester on weekly basis.
They will be graded. After an assignment has been turned in, the solutions to
the problems will be posted below.
Assignments are 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. After you have
used up the two free late days, a penalty of 20% per day will be applied to
each late assignment.
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 makeup a missed quiz or retake a poor quiz during my
office hours within one week after the quiz was given.
Midterm Exams (20% X
2) Two midterm examinations are scheduled on the days
specified on the tentative schedule. Student who are unable to attend an
examination should contact the instructor as early as possible prior to the
examination to discuss the possibility of alternate arrangements. A student who
is absent from an examination may request a makeup examination only if the examination
was missed for a serious reason (such as family emergency, or illness with a
doctor’s note).
Final Exam (25%) Final examination date and time is listed on the tentatitive schedule below. No makeup final.
Grading 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
· Slope fields and integral curves
· Solution techniques for separable and linear ODEs
· Existence and Uniqueness
· Applications and modeling
· Substitution techniques and exact equations
2. Introduction to numerical approximations
· Basic models and equilibrium solutions
· Euler’s method
· RungeKutta method
3. Higher order equations
· 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
· Elimination method
· Eigenvalue method
5. Laplace transform
· Basic properties of the Laplace transform and inverse Laplace transforms
· Solving initial value problems with piecewise continuous input functions
· Impulses and delta functions
6. Power series
· Basic properties and techniques of power series
· Series solutions to an ODE at an ordinary point
Learning Outcomes
·
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
Tentative Schedule
Week 
Monday 
Wednesday 
Fridays 

8/228/26 
Introduction; 1.1. Note for Lecture 1 
1.2. Note for Lecture 2; 
1.3 

8/299/2 
1.4 
1.5 
1.5, Quiz 1; HW 1 due; HW 1 solution 

9/59/9 
Labor Day 
1.6 

9/129/16 
2.1 
2.2 

9/199/23 
Monday's Classnotes ; 2.4 
2.5 
2.5; Quiz 4; HW 4 due; Sample Solution ; 

9/269/30 
2.6 
Review 
Exam 1 Sample Exam 1 (Chapters 12) 

10/310/7 
3.1 
3.3; Quiz 5; HW 5 due 

10/1010/14 
3.5 
3.6; Quiz 6; HW 6 due; HW 6 Solution classnote (Oct 14) 

10/1710/21 
4.2; Quiz 7; HW 7 due; HW 7 Solution 

10/2410/28 
5.1 
5.2; Quiz 8 ; HW 8 due 

10/3111/4 
7.1 
7.3; Quiz 9; HW 9 due. 

11/711/11 
7.3 
7.4; Quiz 10; HW 10 due 

11/1411/18 
Review 
Exam 2. Sample Exam 2, with Solutions (Ch. 35,7.17.4) 
7.5 

11/2111/25 
Thanksgiving Break 
Thanksgiving Break 
Thanksgiving Break 

11/2812/2 
8.1 

12/512/9 
Final Review 

12/1212/16 
For the 8:30 class,
final exam on Tuesday, December 13, 7:309:30am 
For the 11:30 class,
final exam on Friday, December 16, 10:00am12:00pm 
For the 3:30
class, final exam on Tuesday, December 13, 3:005:00 pm 