Math 310 (Ordinary Differential Equations)

Instructor: Frank Gao

Email:; Phone: (208) 885-5274; Office: Brink 322

Course Webpage:
Lecture Time:
 MWF 8:30-9:20 am and 11:30am-12:20pm at NICCOL 006; MWF 3:30pm-4:20pm at TLC 022

Office Hours: Monday 9:30-11:00am, Thursday 1:00-3:00pm; or by appointment
 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 make-up 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 make-up examination only if the examination was missed for a serious reason (such as family emergency, or illness with a doctorís note).


Final Exam (25%) Final examination date and time is listed on the tentatitive schedule below. No make-up final.

 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

        Eulerís method 

        Runge-Kutta 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






 Introduction; 1.1. Note for Lecture 1

1.2. Note for Lecture 2;





1.5, Quiz 1; HW 1 due; HW 1 solution


Labor Day


1.6. Quiz 2; HW 2 due. Solution




2.3; Quiz 3; HW 3 due. Solution


Monday's Classnotes ; 2.4


2.5; Quiz 4; HW 4 due; Sample Solution ;



Review Quiz Solutions before Exam 1; and Classnotes before Exam 1, including solutions to sample Exam 1.

Exam 1 Sample Exam 1  (Chapters 1-2)


3.1 classnote

3.2 classnote (Oct 5)

3.3; Quiz 5; HW 5 due HW 5 Sample Solution


3.4 classnote (Oct 7, Oct 10, Oct 12)


3.6; Quiz 6; HW 6 due; HW 6 Solution classnote (Oct 14) 


3.7 classnote (Oct 17)

4.1 classnote (Oct 19)

4.2; Quiz 7; HW 7 due; HW 7 Solution



5.2 classnote (Oct 26)

5.2; Quiz 8 ; HW 8 due



7.2. Classnotes (Oct 28, Oct 30, Nov 2)

7.3; Quiz 9; HW 9 due.



7.4 Classnotes (Nov 4,Nov 7,Nov 9, Nov 11)

7.4; Quiz 10; HW 10 due



Exam 2. Sample Exam 2, with Solutions (Ch. 3-5,7.1-7.4)



Thanksgiving Break

Thanksgiving Break

Thanksgiving Break


7.5 Class Notes (Nov 28)

7.6 classnote (Nov 30)

8.1 HW 11 (Optional) classnote (Dec 2)


8.2 classnote (Dec 5)

8.3 HW8 solution, HW9 solution, HW10 solution

Final Review Sample Final Exam with Solutions


††††††††††† For the 8:30 class, final exam on Tuesday, December 13, 7:30-9:30am

††††††††††† For the 11:30 class, final exam on Friday, December 16, 10:00am-12:00pm

 ††††††††††† For the 3:30 class, final exam on Tuesday, December 13, 3:00-5:00 pm