Introduction to Differential Equations and Applications

Course Description

Textbook and Lecture Notes

1st order equations: Radioactive nuclei decay, .ps, .pdf, Streamlines, streamfunctions and the velocity potential .ps .pdf
2nd order equations: play with masses and springs (click 2nd order equation, 9,10,11 or 12,mass and spring tool); Method of undetermined coefficients handout .ps .pdf
Laplace Transforms: table .ps .pdf
Systems of ODEs: Review of linear algebra .ps .pdf

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.

(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.

(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.

Mid-term Exam (55 min written examination + take-home exam) Wednesday July 21

(4)The Laplace Transform Definition of Laplace transform and application to initial value problem. Step functions, discontinuities, impulse functions, and the convolution integral

(5)Systems of First Order Linear Equations Brief review of matrices and system formulation. Eigenvalues and linear dependence. Interpretation of eigenvalues in physical systems.

(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. Solution of 2x2 systems by the exponential matrix; Lyapunov Stability.

Learning Objectives and Instructor Expectations

This is an 9 week-long accelerated course. Since 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 taken from the solved problems in BD; therefore you have a valuable resourse in your textbook and you are encouraged to explore additional problems from there.

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.

Teaching Assistant:	If what I say in class is Greek to you, you can also send an e-mail to Justine GunOg Seo Guggenheim 405D justine@amath.washington.edu
Homework and Exams	Homework Due Date	Homework Problem Sets	Homework Solutions
First day of classes	Monday, June 21
Homework#1	due Friday, 6/25	Homework #1 (.ps, .pdf)	HW #1 Solutions (.ps, .pdf)
Homework#2	due Wednesday, 6/30	Homework #2 (.ps, .pdf)	HW #2 Solutions (.ps, .pdf)
Independence Day	Monday, July 5	No class
Homework#3	due Wednesday, 7/7	Homework #3 (.ps, .pdf)	HW #3 Solutions (.ps, .pdf)
Homework#4	due Wednesday, 7/14	Homework #4 (.ps, .pdf)	HW #4 Solutions (.ps, .pdf)
Homework#5	due Wednesday, 7/21	Homework #5 (.ps, .pdf)	HW #5 Solutions (.ps, .pdf)
Mid-term Exam	Wednesday, July 21	practice mid-term(.ps, .pdf)	Midterm exam solutions (.ps, .pdf)
Mid-term Project 1	Wednesday, July 28	Bessel functions ( .ps, .pdf)
Mid-term Project 2	Wednesday, July 28	Legendre polynomials ( .ps, .pdf)
Homework#6	due Wednesday, August 4	Homework #6 (.ps, .pdf)	HW #6 Solutions (.ps, .pdf)
Homework#7	due Monday, August 16	Homework #7 (.ps, .pdf)	HW #7 Solutions (.ps1, .pdf1) (.ps2, .pdf2)
Final Examination	Wednesday, August 18	Practice final exam (.ps, .pdf) Laplace transforms review (.ps, .pdf)

Grading, Exams and Office Hours

You will write the take-home part of the mid-term exam in blue books (or green-books). You will buy 2 of these letter-size blue-books at the beginning of the quarter (available at the university bookstore) and keep them for the mid-term exam. 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.
Books on Reserve in the Engineering Library
Final Exam: Wednesday August 18
The final exam will last 110-minutes, testing your understanding of the material we covered in sections (4), (5) and (6) 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.

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

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