Northeastern University
Mathematics Department


MATH 1225: Differential Equations

Summer 2002

Hours: MTh 1:00-2:15pm, W 2:15-3:20pm
Location: 431 Ryder Hall; Key# 08270

Instructor: Stephen Lovett
Office: 535 Nightingale Hall (NI)
Office Hours: Mon 2:15-40; Wed 3:20-4:30pm
Phone: 373-2080
Email: slovett@lynx.neu.edu

Your computer's date must be accurate.
   

Required Text: Differential Equations, Computing and Modeling, 2nd
by Edwards and Penney


Course Objectives

This is a first course in (ODEs) ordinary differential equations, i.e. differential equations of functions in one variable. We will cover in detail theoretical methods for solving linear first order equations, studying higher order linear equations and using Laplace’s Method. We spend as much time as possible presenting applications for these concepts to physical problems (forced oscillations, population models, electrical circuits, stability, motion with different models for friction.) The difficulties in solving ODEs explicitly, lead us to consider numerical methods for estimating a solution given initial conditions; this is where the computer labs come in.

Chap.TopicHomeworkComments
1.1Intro to Differential Equations3,7,11 p.9 
1.5Linear Equations5-7,12,13,17,20,23 p.52
1.5Applications of Linear Equations33,34,36,37 p.53 
1.4Separable Equations1,6,13,22,25,39,40 p.40  
1.6Homogeneous Equations5,6,9,12,13 p.69  
1.6Bernoulli Equations20,21,23,30 p.70  
2.1Population Models1,6,7,18,20,25 p.84  
2.2Equilibrium and Stability1,3,4,6 p.93  
2.3Velocity-Acceleration Models1-5,9,20 p.103  
3.1Second Order Linear Equations10-15,21,24 p.152 
3.2General Solutions to Linear Equations1,4,13,17,18 p.165 
3.3Constant Coefficients1-9,15,16,20-23,27,31 p.178  
3.4Mechanical Vibrations1-4,13,15,18,20 p.188  
3.5Nonhomogeneous Equations1-4,9,21,24,25,26,31-33 p.204 
3.6Forced Oscillations and Resonance2,3,8 p.216 
3.7Electrical Circuits1,4,7,17,18,21 p.227 
4.2Linear Systems by Elimination1-6 p.264  
7.1The Laplace Transform3,7,12,15,16,19,23,26,29,30 p.454  
7.2Initial Value Problems1,4-7,10,13 p.466  
7.3Translation and Partial Fractions2,3,11,13,14,19,20,27,30 p.476
7.5Periodic Input Functions1,3,8,11,14,29 p.498 
7.6Impulse and Delta Functions1-4 p.510 


Computer Labs

The copmuter labs are intended to provide you with a feel for numerical and computational methods to solutions of differential equations. You should have received a packet bundled with your textbook if you bought it at the NEU bookstore. Of course, feel free to ask me questions on the labs as they are an important part of the course.

The labs will use either MatLab (which) is available on any computer on the NEU common operating evironment or just Excel. As the computer lab in the math department is shut down this summer for upgrading, you will need to use InfoCommons or any other computer center.

The first lab refers to a program called "diffs" that uses Matlab for its computations. You can retrieve this program by clicking here: diffs.zip. Then follow these instructions:

  1. Download the diffs.zip file to anywhere on your machine.
  2. Extract the zip file to the C: drive of your machine. (This will unpack a diffs folder containing the relevant files.)
  3. Open MATLAB.
  4. At the >> prompt, enter
      >>path(path,'C:\DIFFS')
      >>DIFFS
Of course, if you unpack the diffs folder to another directory than the C: drive, simply declare the appropriate path when you get into MATLAB.


Course Policies

  1. Help and Tutoring: There a number of resources for help. The best way is to come see me. During the summer, the math department still offers free tutoring between 9:00am and 5:00pm Mon-Thurs at 544 Nightingale. The school of engineering may also offer special tutoring for engineering students but I'm not sure of their provision for this service over the summer.
  2. Attendance: I do not keep attendance but the student is responsible for keeping up with any changes announced in class, whether or not he or she is present.
  3. Excused Absences: In order to take a make-up a late quiz or exam you must have talked to me first. For any other emergency situations, you will need to bring me valid documentation (from court, doctor,…) of your absence. Notes from family members are not acceptable.
  4. Other Tools: For those who need a few basic calculus reminders, I've placed on the web a pdf file continaing the basic calculus rules. (calcrulz.pdf) You may use this as a help for homework and studying but you won't be allowed to use it during in-class quizzes or exams.
  5. Assignments and Grades: There will be weekly quizzes (no matter how much material is covered), a one-hour midterm, 5 computer labs and a two-hour cumulative departmental final. The final course grade will be calculated as follows:

     
    Homeworks           4%
    Computer Labs10%
    Weekly Quizzes18%
    Midterm Exam28%
    Final Exam40%
  6. Cheating: Those who choose to cheat should consult the appropriate section their Student Handbook or read the university's Academic Integrity Policy prior to doing so. In this class, collaborating on homeworks is not considered cheating but each person must turn in his or her own write-up. Furthermore, the use of an advanced calculator is not considered cheating but strongly encouraged.
  7. If you have any questions, please feel free to talk to me. If my office hours are not convenient for you, please contact me and we can find some other time to meet.