AMATH 351
SLN 1207, MWF 10:30-11:20 LOEW HALL 105
Syllabus
- (1) First Order Differential Equations:
Solution techniques for linear, separable equations
and exact equations.
Modeling of problems in mechanics.
Remarks on existence and uniqueness of solutions.
BD sections: 1.3, 2.1,2.2,2.4,2.6
EXAM #1 on material from par.(1)-30-50 minutes- (2) Second Order Differential Equations: Analytic techniques for homogeneous equations with constant coefficients. Linear independence and characteristic equation. Nonhomogeneous equations and variation of parameters. Problems in mechanical vibrations and electric circuits.
BD all of chapter 3.
EXAM#2 on material from par.(2) -30- 50 minutes- (3)Series Solutions of Second Order Linear Equations : Power series expansion near regular and singular points. Bessel, Legendre and Hermite equations and their occurrence in mathematical physics.
Project, on material from par.(3)
- (4) Nonlinear 2nd order equations, Euler equations Examples from electrostatics and other branches of physics.
- (5)The Laplace Transform Definition of Laplace transform and application to initial value problem. Step functions, discontinuities, impulse functions, and the convolution integral
- (6)Systems of First Order Linear Equations Brief review of matrices and system formulation. Eigenvalues and linear dependence. Interpretation of eigenvalues in physical systems.
- (7) 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. Solution of 2x2 systems by the exponential matrix; Lyapunov Stability.
- (2) Second Order Differential Equations: Analytic techniques for homogeneous equations with constant coefficients. Linear independence and characteristic equation. Nonhomogeneous equations and variation of parameters. Problems in mechanical vibrations and electric circuits.
Final exam (110 minute written examination on material from paragraphs (4)-(7))
Learning Objectives and Instructor Expectations
By the end of the class you will be able to:(1) Identify the class of ODEs you have to solve;
(2) Identify the solution strategy; Find a suitable reference;
(3) Interpret the results and compare with physical intuition;
The contents of the course are themselves demanding, this means you will have to invest a significant amount of time in this course. Thus, class participation, independent reading from the textbook and working out homework problems is essential. In particular the examples I use are not (usually) taken from BD's examples; therefore you have a valuable resourse in your textbook and you are encouraged to explore additional problems from there.
Schedule and Homework
Homework Format Please fill in your answers in the spaces of the h/w sheet (if any); You may use a computer algebra package to check the answers you derived by hand. You may discuss and compare your results with other students in the class but you should provide your own answers.
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.
Teaching Assistant: |
If what I say in class is Greek to you, you can also send an e-mail to Chris Guggenheim 405D curtchr@amath.washington.edu |
Homework and Exams | Homework Due Date | Homework Problem Sets | Homework Solutions |
| First day of classes | Wednesday, September 28 | ||
| First day of classes | Wednesday, September 28 | Extra lecture | 17:30-19:30, LOW 105 BD sections: 1.3, 2.1,2.4 |
| Homework#1 | due Monday, October 3 | Homework #1 (.ps, .pdf) | HW #1 Solutions (.ps, .pdf) |
| Homework#2 | due Wednesday, October 12 | Homework #2 (.ps, .pdf) | HW #2 Solutions (.ps, .pdf) |
| Exam #1 | Monday, October 17 | practice exam(.ps, .pdf) | 2004 exam (.ps, .pdf) Exam#1 solutions (.ps, .pdf) |
| Homework#3 | due Wednesday, October 19 | Homework #3 ( .pdf) | HW #3 Solutions ( .pdf) |
| Homework#4 | due Wednesday, October 26 | Homework #4 (.ps, .pdf) | HW #4 Solutions (.ps, .pdf) |
| Homework#5 | Now due Friday, November 4 | Homework #5 (.ps, .pdf) | HW #5 Solutions (.ps, .pdf) |
| Exam #2 | Monday, November 7 | practice exam(.ps, .pdf) | Exam #2solutions(.ps, .pdf) |
| Veteran's Day | Friday, November 11 | No class | |
| Mid-term Project 1 | due Wednesday, December 7 | Bessel functions ( .ps, .pdf) | |
| Mid-term Project 2 | due Wednesday, December 7 | Legendre polynomials ( .ps, .pdf) | |
| Homework#6 | due Wednesday, November 16 | Homework #6 (.ps, .pdf) | HW #6 Solutions (.ps, .pdf) |
| Homework#7 | due Wednesday, November 23 | Homework #7 (.ps, .pdf) | HW #7 Solutions (.ps, .pdf) |
| Thanksgiving | Friday, November 25 | No class |  |
Homework#8 | due Wednesday, November 30 | Homework #8 (.ps, .pdf) | HW #8 Solutions (.ps, .pdf) | Homework#9 | due Friday, December 2 | Homework #9 | 7.2 #23 |
| week 10 office hrs | Wednesday Dec 7, 11:30-13:00 Kirk |
Friday Dec 9, 11:30:13:00 Kirk |
Homework#10 | due Friday, December 9 | Homework #10 (.ps, .pdf) | HW #10 Solutions (.ps7, .pdf7 .ps9, .pdf9) | Last day of classes | Friday, December 9 |
| Final Examination | Monday December 12 08:20-10:20 Low 105 |
Practice final exam (.ps, .pdf)
Laplace transforms review (.ps, .pdf) |
Final '04 (.ps, .pdf) |
Grading, Exams and Office Hours
Your course grade will be calculated by weighing your Homework, Exams #1,2, Project and Final Exam grades in the proportions 20%, 10%, 10%,10% and 50% respectively. Homework problem sets will be assigned weekly, normally due on WednesdayExams#1,2:
30-50-minute written examination each that will cover material as described in paragraphs (1) and (2) of the Syllabus respectively
Project
It will cover material from paragraph (3) of the Syllabus and will require you to read and review literature recommended by me. You will write the project in green books. You will buy 1 of these letter-size green-books at the beginning of the quarter (available at the university bookstore) and keep them for the project.
Books on Reserve in the Engineering Library to use for the project
Practice exams for each exam will be posted on this site in due time. Before every exam there will be a review session. During the exams, you are allowed the use of a crib sheet (letter-sized, two-sided), and I will bring a transparency with integrals, need be. NO CALCULATORS.
Final Exam: Friday or Monday
The final exam will last 110-minutes, testing your understanding of the material we covered in sections (4), (5), (6) and (7) of the syllabus and emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity. Bring with you: (1) a double-sided sheet of notes (2) the table with the method of undetermined coefficients (3) the table of Laplace Transforms.
Important Note on Office hours
Office hours are hours during which I am guaranteed to be in my office, answering your questions and dealing with problems you may have in this course. Office hours are not time during which you do your homework in my office. Rather, you should use this time to ask questions about problems which you have tried to work out, but got stuck at some point. In other words, you should come to office hours prepared, just like you should come to class prepared.
Extra credit
(1) I will frequently assign some homework problems of extra difficulty for those
wishing to
explore the techniques further and test their understanding.
(2)
Since most of you come from diverse areas of science and engineering, economics etc.
where ODEs are frequently used, in every homework,
you are strongly encouraged to explore your area and find one (1) problem that uses the
techniques of this week's homework (which I will be describing each week). You will
get extra credit for a sound explanation of the origins of the problem and a
full solution
This part of the coursework, prepares you to explore literature
independently of what I say in class, and to learn how to
think on your own.
Furthermore, this is the most enjoyable part of grading for me so
extra credit will be generous here.
You may view your homework and exam grades on-line.
| <kirkinis@amath.washington.edu> | Th Nov 17 19:04:47 PDT 2005 |