Math 0290 *** Differential Equations *** Spring 2012
Instructor: David
Swigon, Thackeray 511, 412-624-4689,
swigon@pitt.edu
Lectures:
MWF 12:00-12:50pm, LAWRN 205
Office
Hours: MW 1:30-3pm, Thackeray 511, or
by appointment.
Grader: Hang
Nguyen, nguyentienhang@gmail.com
, Office hours: TBA
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math0290.html
Prerequisites
Single-variable
calculus (Math 0420, 0450, or equivalent) including Taylor series, linear
algebra (Math 1180, 1185 or equivalent) including eigenvalues and eigenvectors.
Textbook
* Polking, Boggess and Arnold, Differential Equations with Boundary Value
Problems, second edition, Pearson
Prentice-Hall 2006, ISBN 0131862367
* Polking and Arnold,Ordinary Differential Equations using MatLab, Third Edition, Pearson Prentice-Hall , ISBN
0131456792
(Both
available at The Book Center on Fifth Ave.)
Other Materials
You will
need some MatLab add-on software for differential
equations. It can be downloaded from http://math.rice.edu/~dfield/ at Rice University.
Java
applets for pplane
and dfield
programs can be found at http://math.rice.edu/~dfield/dfpp.html
. They run in your browser without the need
for Matlab software.
Grading
Scheme
Homework
Assignments: 20%
Two
Midterm Exams: 40% (20%
each)
Cumulative
Final Exam: 40%
Exam
Policies
Exam dates will be announced ahead of time. Any student with a serious
conflict should alert the instructor ahead of time, before the exam date, to
discuss arrangements and should be prepared to show documentation establishing
validity of the conflict. The time and place of the departmental final exam has
been scheduled by the registrar. According
to the policies of the Department of Mathematics, your final grade may not
exceed your final exam grade by more than one letter grade.
Academic Integrity
Cheating/plagiarism will not be tolerated. Students suspected of
violating the University of Pittsburgh Policy on Academic Integrity will incur
a minimum sanction of a zero score for the quiz, exam or paper in question.
Additional sanctions may be imposed, depending on the severity of the
infraction. On homework, you may work
with other students or use library resources, but each student must write up
his or her solutions independently. Copying solutions from other students will
be considered cheating, and handled accordingly. The
schedule and a list of homework problems will be posted below. Homework
is due at the beginning of a class one week after it was assigned.
Disability Resource Services
If
you have a disability for which you are or may be requesting an accommodation,
you are encouraged to contact both your instructor and Disability Resources and
Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early
as possible in the term. DRS will verify your disability and determine
reasonable accommodations for this course.
|
WEEK |
READING
& PRACTICE (M# = MatLab book) |
TOPICS |
HOMEWORK Collected
on Friday 1wk after assigned |
|
Jan
4 – Jan 6 |
2.1
Number 1-6, 12-15 2.2
Number 1-18, 33-35 M1 |
First
order initial value problems Separation
of variables |
1.1 Number 1, 5, 11 2.1 Number 1, 3, 5, 13,
15 |
|
Jan
9 – Jan 13 |
2.3
Number 8-10 2.4
Number 1-21 M2
Number 15-20 |
Models
of motion First
order linear equations |
2.2 Number 3, 5, 9, 33 2.3 Number 9 2.4 Number 5, 15, 19 |
|
Jan
16 |
M.L.K.
Day (no school) |
||
|
Jan
18 – Jan 20 |
3.1
Number 10-13 3.3
Number 3, 5 M3
Number 1-12 |
Modeling DFIELD |
3.1 Number 10, 13 3.3 Number 3, 5 M3 Number 1 |
|
Jan
23 – Jan 27 |
3.4
Number 1-10 4.1
Number 1-20 4.3
Number 1-36 M4
Number 1-8, 17, 18 |
Second
order homogeneous equations Function
m-files |
3.4 Number 1, 3, 7, 11 4.1 Number 1, 3, 9, 17 4.3 Number 1, 9, 17, 35 |
|
Jan
30 - Feb 3 |
4.4
Number 1-12 4.5
Number 1-29 4.6
Number 1-10 4.7
Number 3-6, 12-15 M5
Number 1-6 |
Nonhomogeneous second order equations |
4.4 Number 11, 12 4.5 Number 1, 5, 11,
15, 19 4.6 Number 1, 3, 5 |
|
Feb
6 – Feb 10 |
6.1
Number 1-5 5.1
Number 1-29 5.2
Number 1-41 5.3
Number 1-36 |
Numerical
Methods Laplace
Transform |
4.5 Number 27, 29 4.7 Number 3, 13, 15
(No need to use the transfer function, find the steady state solution using any
method) 6.1 Number 3, 5 |
|
Feb
13 |
5.4
Number 1-26 |
Laplace
Transform |
|
|
Feb
15 |
Review |
|
|
|
Feb 17 |
|
Midterm Exam I Covers 1.1, 2.1-2.5, 3.1, 3.3,
4.1-4.7, 6.1 |
|
|
Feb
20 – Feb 24 |
5.5
Number 1-25 5.6
Number 1-9 5.7
Number 4-24, 26-31 |
Laplace
Transform methods Convolutions |
|
|
Feb
27 – Mar 2 |
8.1
Number 1-16 8.2
Number 13-16 8.3
Number 1-6 |
Introduction
to systems |
|
|
Mar 5 – Mar 9 |
|
Spring Break |
|
|
Mar
12 - Mar 16 |
9.1
Number 1-8, 16-23 9.2
Number 1-27, 58, 59 |
Constant
coefficient homogeneous 2x2 systems |
|
|
Mar
19 – Mar 23 |
9.3
Number 1-23 9.4
Number 1-12 10.1
Number 1-18 |
Nonlinear
systems; equilibria, linearization, stability Trace-determinant
plane |
|
|
Mar
26 – Mar 30 |
10.2
Number 1-4 10.3
Number 1-16 10.5
Number 1-10 |
Long
term behavior, Nullclines Conserved
quantities |
|
|
Apr
2 – Apr 6 |
12.1
Number 1-17 12.3
Number 1-32 |
Fourier
series |
|
|
Apr
9 – Apr 13 |
13.1
Number 1-9 13.2
Number 1-18 |
Heat
equation Separation
of variables |
|
|
Apr
16 |
Review |
|
|
|
Apr
18 |
Midterm Exam II Covers 5.1-5.7, 8.1-8.3, 9.1-9.3,
10.1-10.2, 12.1,12.3,13.1-2 |
|
|
|
Apr
20 |
Review for final exam |
|
|
|
Wednesday Apr 25 |
|
FINAL EXAM 10:00 - 11:50 am Room: TBA |
|