AMATH 351
SLN 1189, MWF 10:30-11:20, Electrical Engineering I 037
Syllabus
- (1) First Order Differential Equations:
Solution techniques for linear and separable equations.
Modeling of problems in mechanics and population modeling.
Remarks on existence and uniqueness of solutions.
- Ch. 2 : approximately 3 lectures
- (2) Second and Higher Order Differential Equations:
Analytic techniques for homogeneous equations with
constant coefficients. Linear independence and
characteristic equation. Nonhomogeneous equations
and variation of parameters. Problems in vibration
and electrical circuits.
- Ch. 3 : approximately 5 lectures
- (3) Series Solutions of Second Order Linear Equations:
Power series expansion near regular and singular point.
Euler equations. Bessel's equations.
- Ch. 5 : approximately 3 lectures
- (4) The Laplace Transform:
Definition of Laplace transform and application to
initial value problem. Step functions, discontinuities,
impulse functions, and the convolution integral.
- Ch. 6 : approximately 3 lectures
- (5) System of First Order Linear Equations:
Brief review of matrices and system formulation.
Eigenvalues and linear dependence. Interpretation
of eigenvalues in physical systems.
- Ch. 7 : approximately 5 lectures
- (6) Nonlinear Differential Equations and Stability:
Introduction to phase-plane analysis techniques and
critical points. Applications to nonlinear systems such as
the predator-prey model. Periodic solutions, limit cycles,
and chaotic behavior.
- Ch. 9 : approximately 5 lectures
Learning Objectives and Instructor Expectations
Differential equations is a fundamental topic in applied mathematics. The broad nature of the subject means that the course will move quickly, covering a number of topics. I will let you know clearly what you need to learn, what is important and what is not. Students are expected to take an active role in their education by completing homework sets and participating in class.
Homeworks are used to reinforce class lectures, not as a way to introduce material not covered in class. Exams will emphasize basic techniques as applied to simple, fundamental problems. Please note that students should be aware of the policies of the University of Washington's Office of Scholarly Integrity regarding scientific and scholarly misconduct found here.
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
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homework and solution sets,
click here.
| Homework and Exams | Homework Due Date | Homework Problem Sets | Homework Solutions |
| First day of classes | Monday, January 5 | ||
| Homework#1 | due Friday, January 9 | Homework #1 (.ps, .pdf) | HW #1 Solutions (.ps, .pdf) |
| Homework#2 | due Friday, January 16 | Homework #2 (.ps, .pdf) | HW #2 Solutions (.ps, .pdf) |
| Martin Luther King Day | Monday, January 19 | No class | |
| Homework#3 | due Friday, January 23 | Homework #3 (.ps, .pdf) | HW #3 Solutions (.ps, .pdf) |
| Exam Review Session | Friday, January 23 | optional | 5-6:30pm, BLM (Balmer) 206 |
| Office Hours | Monday, January 26 | Bernard Deconinck | GUG 407 9-10am |
| Exam I | Monday, January 26 | ||
| Office Hours | Wednesday, January 28 | Brett Pontarelli | GUG 410 9:30-10:20am |
| Homework#4 | due Friday, January 30 | Homework #4 (.ps, .pdf) | HW #4 Solutions** (.ps, .pdf) |
| Office Hours | Wednesday, February 4 | Sarah Hewitt | GUG 417, 4-5pm |
| Homework#5 | due Friday, February 6 | Homework #5 (.ps, .pdf) | HW #5 Solutions (.ps, .pdf) |
| Exam Review Session | Monday, February 9th | optional | 5-6:30pm BLM(Balmer) 206 |
| Office Hours | Wednesday, February 11 | Bernard Deconinck | GUG 407 9-10am |
| Exam II | Wednesday, February 11 | ||
| Homework#6 | due Friday, February 13 | Homework #6 (.ps, .pdf) | HW #6 Solutions (.ps, .pdf) |
| President's Day | Monday, February 16 | No class | |
| Homework#7 | due Friday, February 20 | Homework #7 (.ps, .pdf) | HW #7 Solutions (.ps, .pdf) |
| Homework#8 | due Friday, February 27 | Homework #8 (.ps, .pdf) | HW #8 Solutions (.ps, .pdf) |
| Homework#9 | due Friday, March 3 | Homework #9 (.ps, .pdf) | HW #9 Solutions (.ps, .pdf) |
| Homework#10 | due Friday, March 12 | Homework #10 (.ps, .pdf) | HW #10 Solutions (.ps, .pdf) |
| Last day of classes | Friday, March 12 | ||
| Exam Review Session | Friday, March 12 | optional | 5-6:30pm room TBA |
| Final Exam | Monday March 15, 8:30 am |
Grading
Your course grade will be calculated by weighing your homework, Exam I, Exam II, and Final grades in the proportions 45%, 15%, 15% and 25%, respectively.Homework problem sets, worth 45% of your final grade will be assigned weekly. Homework is due by 4pm on the due date in the instructor's mailbox (located in GUG 408). Late homework will not be accepted. Solution sets will be posted on the course website once the deadline has passed. The lowest homework score for each student will be dropped. Each remaining homework set is weighed equally according to percentage, making them each worth 5% of your final grade.
Homework should be presented in a clear, professional, and precise manner. The grader is allowed to deduct points for presentation. Every homework should have a header with the student's name, course number, date, homework assignment number, and a list of collaborators.
Sample Homework Header
There will also be two fifty-minute-long exams, each constituting 15% of your grade and a comprehensive final for 25% of your grade.
The test schedule is as follows:
Review sessions for Exam I, Exam II, and the Final will take place Friday, January 23, Monday February 9, and Friday March 12 respectively from 5-6:30pm in Balmer Hall room 206. The review sessions will have an open format.
You are allowed one 8-1/2 by 11 inch sheet of notes for each exam. You will have to turn in your note sheet with your exam, but it will be returned to you with your graded exam.
You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password. Please note this change to our system: Your student ID number should be entered excluding any leading zeros (e.g. 12345 instead of 0012345).
** Updated: February 1, 2004
| <shewitt@amath.washington.edu> | Fri Mar 12 16:07:59 2004 |