MATH524 - Fall 2007 - Computing@AMath.UNC

The Essentials

ID	MATH524
Title	Elementary Differential Equations
Times	MWF 2:00-2:50 PM, Phillips 385
Instructor	Sorin Mitran, mitran (AT) amath.unc.edu
Office Hours	MWF 3:00-4:00 PM, Phillips 307
Description	An introduction to analytical and numerical approaches to ODE's

Syllabus

Linear differential systems.
Power series solutions.
Laplace transforms.
Numerical methods.

Motivation and Objectives

Differential equations describe a wide variety of physical, biological and social phenomena. Knowing how to solve the more frequently encountered examples is an important part of a scientist's training. At the end of the course a student should be able to solve elementary differential equations analytically, recognize more difficult equations and use computer software to find exact and numerical solutions.

Grading Policy

Homework - 10 assignments x 8 exercises per week = 50 points
Computer Applications (CAs) - 2 x 5 points = 10 points
Midterm - 5 problems x 4 points = 20 points
Final - 5 problems x 4 points = 20 points
Extra credit (ECs) - You can choose to draft a report on these two topics:
- Use of symbolic mathematics software to solve ODE systems through the Laplace transform (5 points, due 10/31)
- Study of the Lorenz attractor (5 points, due 12/5)

Mapping of point score to grades

		B+	84-88	C+	67-71	D+	51-55
A	96-	B	79-83	C	62-66	D	46-50
A-	89-95	B-	72-78	C-	56-61	F	0-45

Course Texts and Notes

A First Course in Differential Equations, J. David Logan, Springer, 2000. $28.50 at Amazon.com

Lesson Plan

Date	Text Section	Date	Text Section
8/22	1.1	10/15	4.1
8/24	1.3.1	10/17	4.2
8/27	1.2	10/22	4.3, EC1
8/29	1.3.2	10/24	4.4
8/31	1.3.3	10/26	4.5
9/5	1.3.4-1.3.6	10/29	5.1
9/7	2.1	10/31	5.2
9/10	2.2	11/2	5.3.1,5.3.2
9/12	2.3.1	11/5	5.3.3,5.3.4
9/14	2.3.2, CA1	11/7	5.3.5,5.3.6
9/17	2.3.3	11/9	5.5, EC2
9/19	3.1, 3.2	11/12	6.1
9/21	3.3	11/14	6.1
9/24	3.3	11/16	6.2
9/26	3.4.1,3.4.2	11/19	-
9/28	3.4.3,3.4.4	11/26	6.4, CA3
10/1	3.5	11/28	CA3
10/3	3.6	11/30	Final review
10/5	Midterm review	12/3	Final review
10/8	Midterm review	12/5	Final review
10/10	Midterm Examination Solution	12/14, 12:00 PM	Final Examination Solution

Homework and Projects

Homework is due on Wednesday, handed back the next Monday.

Dates	Exercises	Dates	Exercises
8/22-8/29	p.11:2,3,4,6,8,10,11,16	10/24-10/31	p.138:7,14,15,17, p.145:3a,3b,3c,3h
8/29-9/5	p.37: 1,2,3,4,5,6a,6c,8	11/5-11/12	p.177 3,5,6,7,10,11,12,16
9/5-9/12	p.43: 1, 2a, 2b, 4a, 4b, 4c, p.47: 5, p.50: 6	11/7-11/14	p.196 1,2,4a,4b,4f,5,7,9
9/12-9/19	p.73: 2, p.80:4; Double points: p.80:1,2,3	11/19-12/3	p.227: 6,7,13, p243:8,9,16, p252:4,6
9/19-9/26	p.68: 10,11a,11b,11c; p.94: 1c, 1d, 2,3
9/26-10/3	p.102: 3,4,5; p.115:1a, 2, 3, 4, 5

In addition to the homework, three problems to be solved using mathematical computer systems will be handed out. Draft these using computer typesetting software (pdfLaTeX recommended) and e-mail them to the grading assistant (Shengqian Chen, sqchen@email.unc.edu ) before midnight on the due date.

You can choose any computer software suitable for the problem. Some recommended approaches for each computer application:

Python is very easy to use for this problem and freely available. Download and install Enthought Python. Here's a nice tutorial and another one from someone learning Python because it's the language used in the Civilization computer game :-). To solve the problem you need to write loops and plot data. Matlab also is very useful for this problem and has extensive online tutorials.

Important. The subject line of your e-mail must read: MATH524 CAx Last Name, First Name. Replace x by 1,2,3 corresponding to the appropriate

9/14 - Runge-Kutta methods, due 9/28
- Solution presented in class that models balloon rise up to point where stretching of balloon fabric begins ca1.zip (Matlab code)
11/2 - Boundary value eigenproblem, due 11/16
11/26 - ODE phase portraits, due 12/5