AMATH 351
SLN 10052, MWF 1:10-2:10, SWS 030
(Prerequisites: MATH 125)

Introduction to Differential Equations and Applications

Instructor:

Michael Nivala
Condon 836B
tel: 685-9395
fax: 685-1440
man9@amath.washington.edu
office hours: M,W: 2:10-3:10

Homework

Grades

Announcements

Course description

Textbook

Syllabus

Schedule

Announcements

8/10: The final will cover Sections 3.5-6, 4.1-4, 5.1-2, 6.1-4, Appendix B, and Variation of Parameters. You will be given 1.5 hours (from 1:10-2:40). You are allowed 2 sheets of notes and a calculator.

7/23: Homework #5 has been changed. The 5.2 problems have been moved to Homework #6.

7/16: There is no homework due this week. Extra credit #3 is now posted.

6/23: Extra Credit Homework. Each week I will be assigning one extra credit problem. These problems are not to be handed in with the homework, but are due on the last day of the quarter, 8/17. They will be graded together as one extra homework assignment. Usually the extra credit will consist of problems from the book which use the CD-ROM, but they might also be something I make up. The first extra credit problem is now posted under HW #2.

6/18: HW #1 has been modified: 1.8 #14 has been changed to 1.8 #13.

Course Description

Introductory survey of ordinary differential equations. Linear and nonlinear equations. Taylor series. Laplace transforms. Emphasis on formulation, solution, and interpretation of results. Examples from physical and biological sciences and engineering.

Textbook

P. Blanchard, R. L. Devaney, G. R. Hall, Differential Equations (3rd Edition) (ISBN 0495012653) Brooks/Cole, 2005.

Other (optional) references: W. E. Boyce & R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (8th Edition) (ISBN 0-471-43338-1) John Wiley & Sons, 2004.

Syllabus

(1) First-Order Equations: Introduction to modeling. Analytic techniques: separation of variables, undetermined coefficients, integrating factors. Qualitative technique: slope fields. Numerical technique: Euler's method. Existence and uniqueness. Equilibria and bifurcations.
(2) First-Order Systems: Modeling with systems. Phase plane analysis. Decoupled systems.
(3) Linear Systems: Review of linear algebra. Solutions involving real and complex eigenvalues. Phase plane analysis and the trace-determinant plane.
Midterm Exam
(4) Nonlinear Equations: Equilibrium point analysis. Qualitative methods. Hamiltonian and dissipative systems.
(5) Second Order Equations: Harmonic oscillators. Sinusoidal forcing. Undamped forcing and resonance. Steady state solutions.
(6) Advanced solution techniques: Variation of parameters, Taylor series, and Laplace transforms.
Final Exam

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or

Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Week	Homework and Exams	Homework Due Date	Homework Problem Sets and Readings (From the Blanchard/Devaney/Hall text)
1	First day of classes	Monday, 6/18
	Homework #1	due Friday, 6/22	HW #1: Section 1.1: 3, 4, 15, 16; Section 1.2: 3, 17, 25, 34; Section 1.8: 1, 9, 13, 20; Section 1.9: 3, 7, 13, 19; Reading: Chapter 1
2	Homework #2	due Friday, 6/29	HW #2: Section 1.3 (HPGSolver parts optional): 10, 15, 16, 17; Section 1.4: 6; Section 1.5: 1, 2, 15, 18; Section 1.6: 8, 9, 20, 21, 32, 45, 46; Section 1.7: 2, 12, 17; Extra Credit #1: Section 1.7: 22, 23 Reading: Chapter 2 Sections 2.1-3
3	Independence Day	Wednesday, 7/4	No class
	Homework #3	due Friday, 7/6	HW #3: (HPGSystemSolver parts optional) Section 2.1: 2 (no explanation needed), 7, 8, 19 Section 2.2: 9, 10, 11, 21, 23, 24, 25, 27 Section 2.3: 5, 7, 12a, 19 Section 3.1: 6, 16, 24 (also show that the two solutions are linearly independent using the result of problem 32), 34 Extra Credit #2: Section 2.2: 14, 16, 18 Section 3.1: 10, 12, 15 Reading: Chapter 3 Sections 3.1-5
4	Homework #4	due Friday, 7/13	HW #4: Section 3.2: (In part c of 1-10 just plot the straight line solutions) 1, 2, 3, 6, 7, 8, 9, 10, 12 Section 3.3: 1-8, 10 Section 3.4: 3, 4, 5, 9, 10, 11 Reading: Chapter 3 Sections 3.1-5 (same as last week)
5	Midterm Exam	Monday, 7/16
	No Homework		HW: NONE Extra Credit #3: Read Section 2.5 and do problems 4 and 5. Reading: Chapter 5 Sections 5.1-2
6	Homework #5	due Friday, 7/27	HW #5: Section 3.5: 2, 4, 6, 8, 17, 18 Section 5.1: 2, 4, 5, 6, 8 Reading: Chapter 3 Section 3.6 and Chapter 4 Sections 4.1-4
7	Homework #6	due Friday, 8/3	HW #6: Section 5.2: 1, 2, 3, 6 Section 3.6: 2, 3, 6, 8, 9, 11, 14, 22 Section 4.1: 1, 5, 6, 11, 12, 14 Section 4.2: 1, 2, 7, 12, 15, 17 Extra Credit #4: Choose to read either Section 5.3 or Section 5.4. Do problem 1 from whichever section you chose. Reading: Appendix B and handouts form Boyce and DiPrima
8	Homework #7	due Friday, 8/10	HW #7: Section 4.3: 2, 12, 16, 21, 22 Section 4.4: 6, 7 Boyce and DiPrima: 2, 13 Appendix B: 2, 3, 6 Reading: Chapter 6
9	Homework #8	Not turned in.	HW #8 (This homework is not to be turned in. It is only recomended.): Section 6.1: 7, 9, 11, 13, 15, 17, 19, 21, 23 Section 6.2: 5, 7, 9, 11, 13 Section 6.3: 6, 11, 15, 27, 29, 31, 33 Section 6.4: 3, 5, 7
	Final Exam	Friday, 8/17

Grading

Your course grade will be calculated by weighing your homework, Midterm, and Final grades in the proportions 30%, 35%, and 35% respectively. Homework problem sets will be assigned weekly. All work must be shown. You will be allowed one late homework assignment, with a new due date of one week after the original due date (this does not apply to the last homework which is due on the last day of the quarter, 8/17). No other late work will be accepted.

You may view your homework and exam grades on-line.

<man9@amath.washington.edu>

Thu Jun 16 18:58:26 PDT 2005