MAT 303 (Calculus IV with Applications)

Introduction to Differential Equations

Spring 2010

SUNY at Stony Brook

Most of the fundamental laws and principles of nature are expressed mathematically as differential equations. This course discusses the the basic methods for solving ordinary differential equations, with applications to the physical, biological and social sciences. Particular emphasis is given to linear differential equations and systems of equations.

The prerequisite is completion of one of the standard calculus sequences (either MAT 125-127 or MAT 131-132 or MAT 141-142) with a grade of C or higher in MAT 127, 132 or 142 or AMS 161. The course will rely heavily on material you've learned in Calculus I-II. Familiarity with complex numbers and the basic concepts of linear algebra will be important, so the 200-level classes MAT 203/205 (Calculus III) or AMS 261/MAT 211 (Linear Algebra) are strongly recommended.


Recitation Instructors:

Course Text:

Computer resources:

There are many useful tools to study and understand differential equations with computer and numerical methods. You are free and welcome to explore some of this world, and some of your recitation classes may discuss this further. See also the links below as a sample for further information. However, HW, quizzes and exams will not rely on any use of computers or graphing calculators; at this stage, it is more important that you develop an understanding of the theoretical underpinnings of the subject - how things work.

Homework and Quizzes:

There will be both Homework assignments and quizzes, alternating weekly; one week HW, the next week quiz, etc. There will be HW problems given every week - see the assignments below - and each quiz will contain problems taken from the HW assignments. HW will be collected during the recitations, as determined by your TA; they should always be turned in at the beginning of class. Please, remember that your solutions of the homework problems and quizzes are important documents. You should keep them to the end of the semester.

Although only a random selection of problems on each homework will be graded by your TA, it is important that you do all the HW problems (or at least as many as possible). You should not expect to do well on the exams without the work and experience that goes into solving the HW and quiz problems.

Late homeworks will not be accepted except under very exceptional circumstances. Likewise, no late quizzes will be given. All policies regarding HW, quizzes and your grades for this part of the course are fully decided by your TA.

Grading Policy:

Grades will be computed according to the following percentages:

Homework and Quizzes


Midterm I (Thursday, Feb. 25, 12:50-2:10pm, in class)


Midterm II (Thursday, April 8, 12:50-2:10pm, in class)


Final Exam (Thursday, May 13 5:15-7:45pm)

35% (cumulative)

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 visit your instructor or TA during office hours, or make a separate appointment if necessary. Your instructors will also reply to email, within reason. Another excellent source of help is the Mathematics Learning Center (S240A in the Math Building - basement level), 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

Unless otherwise noted, HW (odd number) you hand in to your TA for grading, while HW (even number) you do,

but do not hand in for grading. Instead, a quiz will be given that week, based on the assigned HW problems.

Week of


Problems Due

Recitation Due Dates

Jan. 25

1.1: Mathematical Models

1.2: General and Particular Solutions


Feb. 1

1.3: Direction Fields
1.4: Separable Equations

1.1: 3,5,13,19,27

1.2: 4,8,15,42

1.3: 2,8,21

HW #1: FMW, Feb 5 - Feb 10

Feb. 8

1.5:Linear First Order Equations
1.6: Subsitution/Exact Equations

1.4: 1,2,3,4,6,47,48

1.5: 1,2,3,12,15

HW #2: FMW, Feb 12 - Feb 17

Feb. 15

2.1:Population Models
2.2: Equilibrium Solutions

1.6: 3,8,17,34,57

2.1: 2,4,10,11

HW #3: FMW, Feb 19 - Feb 24

Feb. 22

2.4:Numerical Methods
Midterm I Exam

No HW or Quiz this week, due to Midterm

No HW due

Mar 1

3.1:Second order linear equations
3.2: General solutions of linear equations

2.2: 9, 21

2.4: 4,8

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

HW #5: FMW, Mar 5 - Mar 10

Mar 8

3.2:General solutions of linear equations
3.3: Homogeneous constant coeff. equations

3.1: 17,20,21,29

3.2: 1,8,18,31

3.3: 4,13,14,34

HW #6: FMW, Mar 12 - Mar 17

Mar 15

3.4:Mechanical Vibrations
3.5: Non-Homogeneous equations

3.3: 18,23

3.4: 1,3,14,15,16

3.5: 1,2,3,9

HW #7: FMW, Mar 19 - Mar 24

Mar 22

3.6:Forced Oscillations and Resonance
3.7: Electrical Circuits

3.5: 6,11,35,38

3.6: 1,8,11,19

HW #8: (Quiz) FMW, Mar 26,Apr 5/7

Apr 5

4.1:First order systems
Midterm II

Apr 12

5.1:Matrices and Linear Systems
5.2: Eigenvalue Method; Homogeneous systems.

4.1: 1,6,11,13,21,22,23

HW #9: FMW, Apr 16 - Apr 21

Apr 19

5.4:Multiple Eigenvalues (briefly)
5.5: Matrix Exponentials

5.1: 14,22,26,35

5.2: 9,12,19,41

5.4: 2,3,11

HW #10: FMW, Apr 23 - Apr 28

Apr 26

5.5:Matrix Exponentials
5.6:Nonhomogenous Systems

5.5: 2,4,10,16,26

5.6: 2,5,14

HW #11: FMW, Apr 30 - May 5