Applied Differential Equations: Math 316

Fall 2006

Section 2 MWF 12:00 - 12:50, MH 213

Instructor:

Irina Vasileva

Office

461 Humanities (4th floor of Humanities Building)

Office Hours

M 15:00-16:00 (Calculus table DSH 3rd floor), W 15:00-17:00 or by appointment

E-mail

vasilevi@math.unm.edu

Web page

http://math.unm.edu/~vasilevi

Phone

277 - 4803

Fax

277 - 5505


Required Text:  Differential Equations by J Polking, A. Boggess and D. Arnold, Second Edition, ISBN 0-13-143738-0

Covered Topics:  First order differential equations; Second order linear and special non-linear differential equations; Laplace transforms; Linear and nonlinear systems of differential equations including a brief study of matrix algebra; Phase plane analysis and stability of linear systems; Modeling and applications. Integrated into the course are computer assignments covering numerical approximations to first order DE, and linear systems of DE. 

Prerequisites:  Calculus I, II, III (recommended)

Grading

Final Exam

25%

2 Midterm Exams

50%

Computer Projects

15%

Quizzes

10%

 

Your grades will be available through Web-CT.

Recommended Problems:  Assigned in class almost every meeting. Not collected.


Quizzes:  Quiz problems will be based on recommended homework problems and will usually be given each week. No make-up quizzes will be given, but the lowest quiz grade will be dropped in case you miss a quiz. In case of severe illness please contact me.

Computer Assignments and Projects:  Several. You will need to use Matlab. No Matlab background is required. ODE using Matlab manual by J. Polking and D. Arnold is recommended (comes with your textbook). Computer assignments are not collected. Computer projects are collected. You will need to turn in printouts of your work. Discussing with others your projects is allowed but the collected material should reflect your knowledge. You will receive step-by-step instructions on what to do.

Midterm Exams:  1 – week 6,  2 – week 12 or 13  

Final Exam:  Cummulative. Tue.  May 9 Section 1:  7:30 – 9:30 a.m. in DSH 225; Section 2: 10:00 a.m. – 12:00 p.m. in DSH 334

Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner.     

Syllabus

Weeks 1-3  2.1 – 2.5, 2.9, 3.1, 6.1, 6.2:  Introduction.1st order DEs. Qualitative solutions. Classification. Direction fields. Numerical methods. Separable and linear equations. Applications.

Week 3-5 4.1, 4.3 - 4.7: 2nd order DEs. General solution of homogeneous equations. Constant coefficient homogeneous equations. Nonhomogeneous equations. Undetermined coefficients. Variation of parameters. Applications (unforced and forced harmonic motion). 

 Week 6  Review. Midterm 1.

Friday - Last day to drop without a grade.

Week 7-8  Ch. 5: Laplace transforms.

Week 9-11 Selected topics from chapters 7, 8 and 6, 9.1 – 9.4, 9.9: Systems of 1st order DEs. 2x2 case. Selected topics from linear algebra. General solution. Phase plane. Fundamental solution matrix. Nonhomogeneous case and Variation of parameters. Numerical solutions. Some applications.

Week 12-13 Review and midterm 2

Week 13-15 Nonlinear systems and stability. Review for the final.

Selected topics from chapter 10. Mainly 10.1, 10.5, 10.6

Week 16 Final  (Dec. 15, 10:00 –12:00)