Math 310 (Ordinary Differential Equations)



Instructor: Frank Gao
; Email: fuchang@uidaho.edu; 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

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
 

8/21-8/25

 Introduction; 1.1

Review Integration; 1.2

1.3

8/28-9/1

1.4

1.5

1.6; Quiz 1; HW 1 due

9/4-9/8

        Labor Day

1.6

2.1; Quiz 2; HW 2 due

9/11-9/15

                 2.2

2.3

2.4; Quiz 3; HW 3 due

9/18-9/22

2.5

Review

Exam 1 (1.1-1.6; 2.1-2.4)

9/25-9/29

2.6

3.1-3.2

3.2; Quiz 4; HW 4 due

10/2-10/6

3.3

3.3-3.4

3.5; Quiz 5; HW 5 due

10/9-10/13

3.5-3.6

3.6-3.7

4.1 Quiz 6; HW 6 due

10/16-10/20

4.2

Review

Exam 2 (3.1-3.7; 4.1-4.2)

10/23-10/27

5.1

5.2

5.2; Quiz 7; HW 7 due

10/30-11/3

7.1-7.2

7.2-7.3

7.3. Quiz 8; HW 8 due

11/6-11/10

7.4

7.4-7.5

7.5; Quiz 9; HW 9 due

11/13-11/17

Review

Exam 3 (5.1-5.2; 7.1-7.4)

TBA

11/20-11/24

Thanksgiving Break

Thanksgiving Break

Thanksgiving Break

11/27-12/1

7.5

7.6

8.1; Quiz 10; HW 10 due

12/4-12/8

8.2

8.3

Final Review

12/11-12/15

Final Exam

Monday 10-12

(for 11:30am class)

Final Exam

Wed 7:30 - 9:30 a.m.

(for 8:30am class)

 

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. HW1 Solution

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

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. HW4 Solution. Quiz 4 Solution

Homework 5 (Due on Friday, Oct. 6): Page 147 (Section 3.1) 11, 13, 15, 26, 37; page 159 (Section 3.2) 5, 9, 13, 21, 24; page 170 (Section 3.3) 5, 8, 14, 18, 21. In case you don't have the correct version of the textbook, you can read the problems here. HW 5Solutions.

Homework 6 (Due on Friday, Oct. 13): Page 183 (Section 3.4) 23; page 195 (Section 3.5) 1,6,10,14,21,24,33,39,49,51; page 206 (Section 3.6) 2,7,29; page 215 (Section 3.7) 11, 13. HW 6 Solutions.

Homework 7 (Due on Friday, Oct. 27): Page 235 (Section 4.1) 4, 5, 19; page 246 (Section 4.2) 7, 12; page 280 (Section 5.1) 13, 14, 15, 16, 18; page 293 (Section 5.2) 2, 3, 5, 6, 8, 9, 17, 18. (Graphing part is optional.) HW 7 Solutions. Class notes on Section 5.2

Homework 8 (Due on Friday, Nov. 3): Page 445 (Section 7.1) 3, 6, 8, 10, 14, 18, 19, 21, 25, 28, 29, 30; page 456 (Section 7.2) 4, 5, 10, 11, 12, 14, 16, 17, 21, 22; page 464 (Section 7.3) 2, 4, 6, 8. (For these four problems, you may hand in together with your next assignment.) HW 8 Solutions.

Class notes on Section 7.1 and Section 7.2

Homework 9 (Due on Friday, Nov. 10): Page 465 (Section 7.3) 12, 13, 17, 27, 30 (and 2, 4, 6, 8 if you have not done so in HW 8) page 473 (Section 7.4) 3, 4, 9, 12, 15, 16, 19, 23, 25; Class notes on Section 7.3 Class notes on Sections 7.4-7.5 page 482 (Section 7.5) 5, 7, 13, 14, 20, 22. HW 9 Solutions.

Homework 10 (Due on Friday, Dec. 1): Page 492 (Section 7.6) 2, 3, 4, 8, 10; page 505 (Section 8.1) 4, 7, 10, 11, 14, 15, 17, 19. page 514 (Section 8.2) (optional) 3, 4, 6, 8. HW 10 Solutions.

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