Math 310 (Ordinary Differential Equations)
Instructor: Frank Gao; Email: firstname.lastname@example.org; Phone: (208) 885-5274; Office: Brink 322
Lecture Time: MWF 8:30-9:20am; 11:30am-12:20 pm; Classroom: NICCOL 006
Office Hours: Monday, Wednesday 10:30-11:20 am, Thursday 1-3 pm; or by appointment.
Textbook: Differential Equations and Boundary Value Problems, by Edwards, Penney and Calvis, 5th edition
Homework (20%) Homework will be assigned during the semester on weekly basis. Homework is due at the beginning of the class on the due date. A penalty of 20% per day will be applied for late homework.
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. A missing quiz will be counted as 0, and there are no make-up quizzes. However, the lowest quiz score will be dropped.
Midterm Exams (15% X 3) Three midterm examinations are scheduled on the days specified on the tentative schedule. A makeup examination is possible only if you get my permission before the examination, or for extraordinary circumstance. In the latter case, a written note, such as a doctor’s note, is usually required.
Final Exam (20%) Final examination is scheduled on dates
specified on the tentative schedule. 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%).
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 and improved 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)
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
Homework 1 (Due on Friday, Sept 1): Section 1.1 (page 8) 10, 15, 20 (do not graph it), 22 (do not graph it); Section 1.2 (page 15) 5, 6, 7, 10; Section 1.3 (page 26) 23, 24; Section 1.4 (page 40) 3, 12, 17, 20.
Here is the codes I used in class to generate a slope field for f(x,y)=x-y. You can modifiy it to do Problems 23 and 24 in Section 1.3: f=@(x,y) x-y; [X,Y]=meshgrid(-3:0.2:3,-3:0.2:3); slope=f(X,Y); L=sqrt(1+slope.^2); quiver(X,Y,1./L, slope./L, 0.55); axis square tight
If you find that the code does not work for Problem 23. I have no idea. However, you can try the following alternative codes instead. f=@(x,y) x-y; x=-3:0.2:3; y=x; [X,Y]=meshgrid(x,y); for i=1:length(x) for j=1:length(y) slope(i,j)=f(x(i),y(j)); end end L=sqrt(1+slope.^2); quiver(X,Y,1./L, slope./L, 0.55); axis square tightHW1 Solution
Homework 2 (Due on Friday, Sept 8): Section 1.4 (page 40) 26, 32; Section 1.5 (page 53) 3, 5, 11, 13, 23, 36; Section 1.6 (page 69) 5, 6, 13, 18, 31, 33, 49.HW2 Solution
Homework 3 (Due on Friday, Sept 15): Page 74: 3, 5, 7, 11, 12, 35; Section 2.1 (page 82) 3, 4, 5, 7; Section 2.2 (page 91) 3, 7 (For these two problems, use the exact solutions to draw curves for the phase diagrams. For Problem 3, use x(0)=4.5, 3.8, 2, -3. For Problem 7, use x(0)=4,3,-1,-4); Section 2.2, 8, 11 (Do not graph for these two problems); Section 2.3 (page 100) 2.HW3 Solution
Homework Assignment 4 (Due on Friday, Sept 29). Note that most of the codes you need to do the problems are included in the sample solutions at the end of the assignment. But you need to define functions ImprovedEuler and RungeKutta and call them when needed. If you need help on using Matlab, I will be happy to help you.