Math 0290 *** Differential Equations *** Spring 2012
Instructor: David
Swigon, Thackeray 511, 4126244689,
swigon@pitt.edu
Lectures:
MWF 12:0012:50pm, LAWRN 205
Office
Hours: MW 1:303pm, 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
Singlevariable
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
PrenticeHall 2006, ISBN 0131862367
* Polking and Arnold,Ordinary Differential Equations using MatLab, Third Edition, Pearson PrenticeHall , ISBN
0131456792
(Both
available at The Book Center on Fifth Ave.)
Other Materials
You will
need some MatLab addon 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, 4126487890 or 4123837355 (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 16, 1215 2.2
Number 118, 3335 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 810 2.4
Number 121 M2
Number 1520 
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 1013 3.3
Number 3, 5 M3
Number 112 
Modeling DFIELD 
3.1 Number 10, 13 3.3 Number 3, 5 M3 Number 1 
Jan
23 – Jan 27 
3.4
Number 110 4.1
Number 120 4.3
Number 136 M4
Number 18, 17, 18 
Second
order homogeneous equations Function
mfiles 
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 112 4.5
Number 129 4.6
Number 110 4.7
Number 36, 1215 M5
Number 16 
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 15 5.1
Number 129 5.2
Number 141 5.3
Number 136 
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 126 
Laplace
Transform 

Feb
15 
Review 
5.1 Number 7, 13, 15,
29 5.2 Number 5, 11, 19,
29 5.3 Number 3, 7, 11, 19 

Feb 17 

Midterm Exam I Covers 1.1, 2.12.5, 3.1, 3.3,
4.14.7, 6.1 

Feb
20 – Feb 24 
5.5
Number 125 5.6
Number 19 5.7
Number 424, 2631 
Laplace
Transform methods Convolutions 
5.4 Number 7, 11, 21 5.5 Number 1, 3, 11, 17 5.6 Number 2, 3, 5, 7 
Feb
27 – Mar 2 
8.1
Number 116 8.2
Number 1316 
Introduction
to systems Geometrical
interpretation of solutions 
5.7 Number 6, 8, 10 8.1 Number 5, 7, 13, 15 8.2 Number 11, 13, 15 
Mar 5 – Mar 9 

Spring Break 

Mar
12  Mar 16 
8.3
Number 16 9.1
Number 18, 1623 9.2
Number 127, 58, 59 
Qualitative
analysis Constant
coefficient homogeneous 2x2 systems 
8.3 Number 1, 3, 5 9.1 Number 3, 5, 17, 19 9.2 Number 3, 17, 23,
59 
Mar
19 – Mar 23 
9.3
Number 123 9.4
Number 112 10.1
Number 118 
Nonlinear
systems; equilibria, linearization, stability Tracedeterminant
plane 
9.3 Number 11, 13, 15,
17, 21, 23 9.9 Number 1, 3, 13, 15 
Mar
26 – Mar 30 
10.2
Number 14 10.3
Number 116 10.5
Number 110 
Long
term behavior, Nullclines Conserved
quantities 
10.1 Number 3, 5, 7 10.2 Number 1, 3 10.3 Number 3, 7, 11 
Apr
2 – Apr 6 
12.1
Number 117 12.3
Number 132 
Fourier
series 
12.1 Number 5, 7, 13,
17 12.3 Number 9, 17, 21,
29 
Apr
9 – Apr 13 
13.1
Number 19 13.2
Number 118 
Heat
equation Separation
of variables 

Apr
16 
Review 


Apr
18 
Midterm Exam II Covers 5.15.7, 8.18.3, 9.19.3,
10.110.2, 12.1,12.3 


Apr
20 
Review for final exam (Since
the old finals followed different syllabus, our final may have different
format and cover different material.) 


Wednesday Apr 25 

FINAL EXAM 10:00  11:50 am Room: 121 Lawrence Hall 
