Math 310 (Ordinary Differential Equations)


Office Hours Monday 9:30-11:00am, Thursday 1:00-3:00pm; or by email appoitment fuchang@uidaho.edu

Lecture time MWF 11:30am-12:20 pm, MCCL 209

Textbook Differential Equations and boundary value problems, by Edwards and Penney, 4th edition

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 doctor’s note.

Final Exam (25%) Final examination is scheduled on Friday, December 20, 2013, 10:00 am—12:00 pm. No make-up finals.

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%).

Tentative Schedule
Week
 
Monday
 
Wednesday
 
Fridays
 
8/26-8/30 Introduction; 1.1. Lecture 1
1.1-1.2; Lecture 2
1.2-1.3
9/2-9/6 Labor Day; no class
1.3
1.4
9/9-9/13 1.4-1.5; HW 1 due, HW 1-part B. HW 1 Solution
1.5
1.6; Quiz 1.
9/16-9/20 1.6, Chapter 1 review; HW 2 due. HW 2 Solution 2.1
2.2; Quiz 2
9/23-9/27 2.3; HW 3 due HW 3 Solution
2.4
2.4; Quiz 3
9/30-10/4 2.4-2.5; HW 4 due HW 4 Solution
2.6
Review; Quiz 4. Sample Exam 1 Solutions to Sample Exam 1 and Quizzes
10/7-10/11 Exam 1(Chapters 1-2
3.1
3.2
10/14-10/18 3.3; No HW 5 (HW 5 will be combined with Quiz 5 as a take home quiz) with some hints
3.4
3.5; Combined HW 5 and Quiz 5.
10/21-10/25 3.6; HW 6 due HW 6 Solution
3.7
Chapter review; Quiz 6
10/28-11/1 4.1;
4.2 HW 7 due HW 7 Solution
5.1; Quiz 7
11/4-11/8 5.2;
7.1
7.2; Quiz 8; HW 8 due
11/11-11/15 Review
Exam 2 (Chapter 3-5) Solution to Sample Exam and Quizzes 5-8
7.3
11/18-11/22 7.4;
7.5
7.5; HW 9 dueQuiz 9
HW 9 Solution
11/25-11/29 Thanksgiving Break
Thanksgiving Break
Thanksgiving Break
12/2-12/6 7.5-7.6;
7.6
8.1; HW 10 due; Quiz 10
HW 10 Solution
12/9-12/13 8.2
An example on power series solution
8.3
Final Review
Sample Final
with Solution
Solution to Retake Quizzes
12/16-12/20

Final Exam, 10am-12pm

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
• Euler’s method
• Runge-Kutta method

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
• Applications

4. Systems of ODEs (Chapter 4: sections 4.1 – 4.2; chapter 5: sections 5.1 – 5.2)---
• Elimination method
• Eigenvalue method

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

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