Instructor: Dr. Sharon Crook
323 Neville Hall, 581-3919
email: crook@math.umaine.edu
Office Hours: MWF 10-11 or by appointment
Texts: Differential Equations by Polking,
Boggess, and Arnold, Prentice Hall Publishers
Ordinary Differential Equations using MATLAB, Polking
and Arnold, Prentice Hall (free with above text)
Description: This course will introduce
methods for determining the solutions to differential equations and
will also cover the theory underlying these methods. We will use both
analytical and computational techniques. We will also study qualitative
methods for analyzing linear and nonlinear differential equations.
Grading: One-period
tests: 45%
Projects, Homework, & Computer Labs:
40%
Final Exam: 15%
All homework, labs, and projects must
be neatly done. No late assignments will be accepted. Make-up exams
require permission in advance. You may work together on homework,
labs, and projects but you must do the work cooperatively. For some
of the assignments, you will be required to work in groups.
If you wish to request an accommodation for a disability, please contact me or Ann Smith, Coordinator of Services for Students with Disabilities (Onward Building, 1-2319) as early as possible in the semester.
Technology: We will use the computer program MATLAB throughout the course. MATLAB is available on the computers in the Mathematics Department computer lab (Room 110) as well as in the computer labs in the Electrical Engineering Department. A student version is available at low cost and is a good investment for anyone in this course (particularly engineering, physics, and math majors). You will be given additional information throughout the semester.
This syllabus will be updated throughout the semester. For changes, see my website under courses or go to http://www.umemat.maine.edu/faculty/crook/courses/mat259/mat259.html.
At the end of the semester, we will cover power series solutions. For
the notes on power series solutions click here.
| MON | 1/12 |
1.1-1.3: Introduction to DEs & Review | 1.1:1-11 1.3:1,3,9,11,15,19,23,25,27 | |
| WED |
1/14 |
2.1 & 2.2: Solutions and Separable
Equations |
2.1:1,3,5,13,17,19 2.2:3,5,13,15
Lab#1 |
|
| FRI |
1/16 |
Finish Separable Equations |
Lab#2 2.1:21,23,25,27,31,33 |
|
| MON |
1/19 |
No Class |
||
| WED |
1/21 | 2.4 Linear Equations |
2.4:1,3,5,7,13,15,19,21,28 |
|
| FRI | 1/23 | Finish 2.4 & Start 2.6 Exact Equations |
2.6:1,3,5,7,13,15,19,21, 27,28,29 |
|
| MON | 1/26 | Finish 2.6 | Lab #3 |
|
| WED | 1/28 | 2.7 Existence & Uniqueness |
2.7:7,9,11,13,15
21,25,27,29 |
|
| FRI | 1/30 | 2.9 Stability |
2.9:1,5,7,8,9,10,11,17,19,23,25 |
|
| MON | 2/2 | 3.1 Population Models |
3.1:1,3,5,9,11,15,19
Project 1 Assigned |
|
| WED | 2/4 | 6.1 & 6.2 Runge Kutta
Numerical Method |
6.1:3,9,14 6.2:3 Lab#4 |
|
| FRI | 2/6 | 6.5 A Cautionary Tale &
Review |
||
| MON | 2/9 |
EXAM 1 |
||
| WED | 2/11 | No Class |
||
| FRI | 2/13 | 7.1 Intro to Matrices and 7.2 |
7.2:5,7 |
|
| MON | 2/16 | 7.3 Solutions & 7.4 Properties
of Solution Sets |
7.3:1,3,5,9,13; 7.4:1,3,5,7,13,15,17,19,21 |
|
| WED | 2/18 | 7.5 Subspaces |
7.5:5,7,11,13,15,19,21,23,29,31,37,39 |
|
| FRI | 2/20 | 7.6 Determinants |
7.6:17,19,21,23,25,27,31,33,35,50,51;
Project 1 Due Lab#9 |
|
| MON | 2/23 | 4.1 Second Order Equations & 4.2 Systems |
4.1:1,3,5,7,11,13,14,15 4.2:1,3,5 |
|
| WED |
2/25 | 4.3 Linear, Homogeneous Equation |
4.3:1,3,5,13,15,17,29 |
|
| FRI | 2/27 | Finish 4.3 |
4.3:7,9,11,19,21,27 |
|
| MON |
3/1 |
Spring Break |
||
| MON | 3/15 | 4.5 Inhomogeneous Equations |
4.5:1,3,5,7,11,15,19,21,25 |
|
| WED | 3/17 | 4.6 Variation of Parameters |
4.6:1,3,5,7,13 |
|
| FRI | 3/19 | 8.1 Intro to Systems & 8.2 Geometric Interpret. |
8.1:3,5,9,13,23,27 8.2:13,14,15,16,17,18,19,20,21 Lab
#6 |
|
| MON | 3/22 | 8.3 Qualitative Analysis & 8.4 Properties of Linear Systems |
8.2:26,27,28
8.3:1,3,5,7,11 8.4:1,3,7,9,15,21 |
|
| WED | 3/24 | EXAM 2 |
||
| FRI | 3/26 | No Class |
Catch up! |
|
| MON | 3/29 | 9.1 Linear Systems |
9.1:1,3,5,9
Lab#7 |
|
| WED | 3/31 | 9.2 Planar Systems |
9.2:3,9,22,23,25,29,31,37,39,43,45 |
|
| FRI | 4/2 | 9.3 Phase Portraits |
9.3:11,13,15,17,19,25,27,29,31,35,36,37 |
|
| MON | 4/5 | 9.4 Higher Dimensional Systems |
9.4:9,11,17,21,27,37,39,45 |
|
| WED | 4/7 | 9.5 Exponentiation of a Matrix |
9.5:17,19,25,27,29 Lab#10 |
|
| FRI |
4/9 | 9.6 Qualitative Behavior of Linear Systems |
9.6:1,3,7,11,13,17,19 |
|
| MON | 4/12 | 10.1 Linearization |
10.1:1,3,5,7,9,11,13,15,17
Project 2 Assigned |
|
| WED | 4/14 | 10.2 Long-term Behavior of Solutions |
10.2:1-21 odd |
|
| FRI | 4/16 | 10.3 Invariant Sets and Nullclines |
10.3:1-17 odd Lab#11 |
|
| MON | 4/19 | 10.4 Long-term Behavior of Planar Systems |
10.4:1-23 odd |
|
| WED | 4/21 | Power Series Solutions |
Power Series Supplement Problems |
|
| FRI | 4/23 | Power Series Solutions |
Power Series Supplement Problems |
|
| MON | 4/27 | Project 2 Due in Class |
||
| WED | 4/28 | Maine Day |
||
| FRI |
4/30 |
Power Series Solutions |
Power Series Supplement Problems |
|
| MON |
5/3 |
Final Exams Start |