MAT 303 (Calculus IV with Applications) Spring 2009

Introduction to Differential Equations

Spring 2008

SUNY at Stony Brook

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 125-127 or MAT 131-132). The 200-level 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.

Course Text:

Computer resources:

Homework and Quizzes:

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.

Grading Policy:

Grades will be computed according to the following percentages:





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 11:00-1:30pm)

30% (cumulative)

The first midterm letter grades.

The second midterm letter grades.

No make-up 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 (A-125 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; 632-6748/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.

Schedule of Topics

(Note: This schedule is tentative and may be revised at a later date.)

Week of


Problems Due


additional problems

Jan. 26

1.1: Mathematical Models

1.2: General an Particular Solutions

Feb. 2

1.3: Direction Fields
1.4: Separable Equations

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 First-Order Equations
1.6: Substitution Methods and Exact Equations



Feb. 16

2.1: Population Models
2.2: Equilibrium Solutions

1.5: 2,12,24,36

1.5: 3,9,23,35

1.6: 3,9,13,17,31,37

Feb. 23

2.3: Acceleration-Velocity Models

2.4: Euler's Method

2.1: 3,11,12,20
Computing Project, parts A and B

2.2: 2,9,21

2.1: 1,18

2.2: 1,3,11

March 2

Practice Midterm I

Practice Midterm I solutions,problems 1,2,3

Practice Midterm I solutions,problem 5

Midterm I Th, Feb. 26

2.5: More on Euler's Method

March 9

2.6: The Runge-Kutta Method

3.1: Second-Order Linear Equations
3.2: General Solutions of Linear Equations

2.3: 2,4,10,22,23

2.4: 4,8,13

2.3: 3,5,11,20

2.4: 10,14

March 16

3.3: Homogeneous Equations with Constant Coefficients
3.4: Mechanical Vibrations

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

3.1: 3,9,15,39,45

March 23

3.5: Nonhomogeneous Equations
3.6: Forced Oscillations and Resonance

3.3: 8,24,40

3.3: 9,15,25

March 30

4.1: First-Order 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

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
7.2: Transformation of Initial value Problems



April 27

6.1: The Phase Plane
6.2: Linear and Almost Linear Systems

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
6.2: 11,14,17

6.1: 2,4,6,8
6.2: 13,15,17