Math 310 (Ordinary Differential Equations)

Office Hours Monday, Tuesday 2:30-4:30 pm; Thursday 9-10 am; or by appointment fuchang@uidaho.edu

Lecture time MWF 1:30-2:20 pm, REN 127

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

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 doctor’s 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 doctor’s note.

Final Exam (30%) Final examination is scheduled on Monday, May 6, 12:30 am—2:30 pm.

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%).

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Tentative Schedule

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Week   Monday   Wednesday   Fridays   1/9-/1/11   Introduction; 1.1 Lecture 1 1.1-1.2 Lecture 2 Sample Homework Solution 1/14-1/18 1.2-1.3 1.3 1.4 1/21-1/25 Martin Luther King. No class 1.4-1.5; HW 1 due Solutions 1.5; Quiz 1. Quiz 1 Solution due Solutions 1/28-2/1 1.6 1.6, chapter review; HW 2 due Sample Solution HW 2 Solution 2.1; Quiz 2 2/4-2/8 2.1-2.2 2.2-2.3; HW 3 due Sample Solution HW 3 Solution 2.3; Quiz 3 2/11-2/15 2.4 2.4-2.5; HW 4 due Sample Solution HW 4 Solution 2.6; Quiz 4 2/18-2/22 Presidents’ Day. No class Chapter 1-2 review Exam 1 (covers chapters 1-2) 2/25-3/1 3.1 3.1-3.2; HW 5 due 3.2-3.3; Quiz 5. Sample Quiz 5 3/4-3/8 3.3-3.4 3.5; HW 6 due Sample Solution HW 6 Solution 3.6-3.7; Quiz 6 3/11-3/15 Spring Break Spring Break Spring Break 3/18-3/22 4.1 4.2; HW 7 due 5.1; Quiz 7 3/25-3/29 Withdraw Deadline; 5.2 Chapter 3-5 review Exam 2 (covers chapters 3-5) 4/1-4/5 7.1 7.1-7.2; HW 8 due HW 8 Solution 7.2; Quiz 8 4/8-4/12 7.3 7.3-7.4; HW 9 due 7.4; Quiz 9 4/15-4/19 7.5 7.5-7.6; HW 10 due 7.6; Quiz 10 4/22-4/26 8.1 8.1-8.2; HW 11 due 8.2; Quiz 11 4/29-5/3 8.3 chapter review Final Review 5/6-5/10 Final Exam (12:30 pm-2:30 pm)

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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