This course is an introduction to differential equations, with particular emphasis on scientific applications. Topics we will cover include homogeneous and non homogeneous linear equations, systems of equations, the Laplace transform, series solutions to equations and nonlinear systems. Numerical and graphical methods will play an important role throughout the semester; these will be implemented using a variety of computer and calculator technologies. The prerequisite is completion of one of the standard calculus sequences (either MAT 125127 or MAT 131132). The 200level courses MAT 203/205 (Calculus III) and MAT 211 (Linear Algebra) are not required, but it is strongly recommended that you have had some exposure to basic ideas in multivariable calculus and linear algebra.
Instructor: Mikhail Movshev
Office Location: 4109 Math Tower
Email: mmovshev ad math dot sunysb dot edu
Web site: http://www.math.sunysb.edu/~mmovshev
Office hours: Wed 1:003:00 in 4109 Math Tower
MAT 303 
Lectures and Recitations 
Final Exam: Tuesday May 19, 11:00am1:30pm in Physics P118 
LEC 1 
41259 
Tu,Th 
12:50pm 2:10pm 
Physics 
P118 
Mikhail Movshev 
R01 
41005 
F 
11:45am12:40pm 
Physics 
P128 
Joseph Malkoun 
R02 
49316 
W 
11:45am12:40pm 
Physics 
P128 
Andrew Bulawa 
R03 
58873 
M 
10:40am11:35am 
Physics 
P129 
Joseph Malkoun 
Recitation Instructors:
R01,R02: Joseph Malkoun
Email: malkoun ad math dot sunysb dot edu
Office hours: Wed 2:003:00 in 2112 and MLC Tue 5:007:00
R 03: Andrew Bulawa
Email: abulawa ad math dot sunysb dot edu
Office: 2121 Math Tower
Office hours: Wednesday 910, MLC hours are Tuesday 46
Differential Equations and Boundary Value Problems, by C. H. Edwards, Jr. and D. E. Penney (PrenticeHall, Inc.), Fourth Edition.(Note, that problem sets in different editions do not coincide)
DiffEqWeb a graphical ordinary differential equation solver written by Simo Kivelä and Mika Spåra of the Helsinki University of Technology.
Programs for Euler's method and slope field generation for graphing calculators (Texas Instruments TI82, TI85 and Sharp EL9300, EL 9200).
MAPLE reference pages. Elementary numerical and graphical examples (these pages were prepared by Stewart Mandell for use in our course MAT 126 several years ago). If you need help getting used to MAPLE, these are a good place to start.
Some additional reference pages which describe how to use MAPLE to investigate properties of differential equations :
a beginning tutorial (introduces you to the syntax of MAPLE)
Homework assignments will be collected during the recitations ; they should always be turned in at the beginning of class. Please, remember that your solutions of the homework problem are important documents. You should keep them to the end of the semester. A random selection of problems on each homework will be graded by the TA. In addition, I will also provide a list of suggested extra problems; these will not be collected but I strongly recommend that you attempt them as well, particularly if you find yourself having difficulty with the material in a specific section.
Approximately twice a month there will be a short quiz, usually administered during a lecture section.
Late homeworks will not be accepted except under very exceptional circumstances. Likewise, no late quizzes will be given. At the end of the semester, I will drop your lowest homework and your lowest quiz grade.
Grades will be computed according to the following percentages:
Homework 
20% 
Quizzes 
10% 
First Midterm (Th February 26 in class) 
20% (will cover 1.1,1.2,1.3,1.4,1.5,1.6,2.1) 
Second Midterm (Th April 16 in class) 
20% (will cover 2.2,2.3,2.4,2.6,3.1,3.2,3.3,3.4,3.5) 
Final (Tuesday, May 19 11:001:30pm) 
30% (cumulative) 
The first midterm letter grades.
The second midterm letter grades.
No makeup exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.
Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to send email, either to myself or to the TA. It is not always easy to explain mathematical concepts via email, however, so if your question is a mathematical one, you should probably ask me in person during my office hours. Another excellent source of help is the Mathematics Learning Center (A125 in the Physics Building), which is staffed by advanced math majors and graduate students daily. For a schedule of their hours, check their website.
Students with Disabilities: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 6326748/TDD. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.
(Note: This schedule is tentative and may be revised at a later date.)
Week of 
Topics 
Problems Due 
Suggested additional problems 

Jan. 26 
1.1: Mathematical Models 1.2: General an Particular Solutions 


Feb. 2 
1.3: Direction Fields 
1.1: 6,10,16,24,34,40 1.2: 6,8,16,22 
1.1: 9,11,15,21,31,35 1.2: 5,7,17,23 
Feb. 9 
1.5: Linear FirstOrder Equations 


Feb. 16 
2.1: Population Models

1.5: 2,12,24,36

1.5: 3,9,23,35 1.6: 3,9,13,17,31,37

Feb. 23 
2.3: AccelerationVelocity Models 2.4: Euler's Method 
2.1: 3,11,12,20 2.2: 2,9,21 
2.1: 1,18 2.2: 1,3,11 
March 2 
Practice Midterm I solutions,problems 1,2,3 Practice Midterm I solutions,problem 5 Midterm I Th, Feb. 26



March 9 
2.6: The RungeKutta Method 3.1: SecondOrder Linear Equations 
2.3: 2,4,10,22,23

2.3: 3,5,11,20 2.4: 10,14

March 16 
3.3: Homogeneous Equations with Constant Coefficients

3.1: 4,10,14,34,40,46

3.1: 3,9,15,39,45

March 23 
3.5: Nonhomogeneous Equations 
3.3: 8,24,40

3.3: 9,15,25

March 30 
4.1: FirstOrder Systems of Equations 4.2: The Method of Elimination

3.5: 6,14,20,38,5538,55

3.5: 3,17,33,49

April 6 
Spring Break Practice Midterm II Solutions Part I Practice Midterm II Solutions Part II pr.3 pr.5 pr.7 pr.8.1



April 13 
5.1: Matrices and Linear Systems Midterm II Th, April 16 
4.1: 2,8,14,18,23 4.2: 8,10,22 
4.1: 1,7,11,15 4.2: 3,9,21 
April 20 
5.2: The Eigenvalue Method 5.4: Multiple Eigenvalue Solutions 7.1: Introduction to Laplace Transforms 


April 27 
6.1: The Phase Plane 
5.2: 4,12,18,30,38 5.4: 2,8,12,20 7.1: 1,4,8,14,20,38

5.2: 1,7,13,17,29 5.4: 1,3,7,13 7.1: 3,7,13,19,37

May 4 
Review Practice Final Solutions. Problems 1. 3, 5. 6, 8. 10, 11,and even moresolutions 
6.1: 1,3,5,7 
6.1: 2,4,6,8 