Math
221-- Differential
Equations
Spring 2006
Instructor:
Petronela Radu
Office: AVH 239
Phone: 472-9130
E-mail: pradu@math.unl.edu
Office Hours: 2:30
- 4:00 pm Monday & Wednesday or by appointment
Schedule
of classes: 11:30 -12:20 MWF ---- OLD H 304
Text: C. Henry Edwards and
David E. Penney.
Differential Equations : Computing and Modeling, Third Edition,
Pearson Education, Inc.
Final Exam: A
comprehensive
final examination is given on Monday, May 1 (10:00-12:00)
in Oldfather Hall 304
You
must arrange your personal schedule to permit you to take the final
exam
at the regularly scheduled time.
Computer Lab / Calculators:
Students can use the computers from the Mathematics
Department
Computer Laboratory in Avery 18
with their university account (go to http://activedir.unl.edu). In
this section of the course, we will use Maple for
gaining more insight into the
material. Student versions of
Maple or Mathematica are available for purchase in the
campus computer shop. During the semester at least two or three
lectures will be held in the Computer Laboratory (Avery 18), so we will
get familiarized with simple programming in Maple and also with using
the computer to solve differential equations. The use of calculators will be allowed only
on some exams or quizzes
and these occasions will be announced at least few days in advance. The
use of any
other electronic device (cell phones, ear pieces etc.) is not
permitted during classtime or during exams.
Syllabus:
You
can find here a
copy of a tentative syllabus. The
suggested homework problems from this list will not be collected.
Daily Work: The homework
will
be announced in class and posted on the web site every week. The
homework will be collected
and two problems selected by the instructor will be graded. Each
homework is
worth 15 points. The best 10 scores from the homework assignment will
count towards the final grade.
Homework:
Week 01/9 -
01/13
1.1
pg.
8-9: 3, 9, 16, 22, 25, 30, 35
(due 01/19 - 9 am)
1.2 pg.
16-18: 3, 6, 10, 14, 22*, 25, 30*
1.3 pg. 26-29: 2, 8, 12, 15, 21, 27*
Week 01/16-
01/20
1.4 pg. 41-44: 5,
16, 17, 24, 35,
38, 49*
(due 01/25)
1.5 pg. 54-56: 3, 11, 16, 21*, 30,
37
Week 01/23 -
01/27
1.6
pg. 71-72: 7, 14, 29, 37*, 47*
(due 02/01)
2.1 pg.
86-88: 9*, 18, 21, 24
Week 01/30 - 02/03 2.2 pg.
96-97: 6, 10*, 21
(due
02/08)
2.3
pg. 106-107: 1, 2* ,4 ,20
2.4 pg. 119-120: 4, 7 *
Find the exact solution and the required approximation in 12, 13, 15.
Find the approximation for
h=.025 in 19, 23.
Weeks 02/06 - 02/17 3.1 pg.
155 -157: 6, 16, 18, 22, 27,35, 52*
(due 02/17)
3.2 pg. 167 -169: 3, 18, 24*, 26, 39*
Additional Homework
Week 02/20 - 02/24 3.3 pg. 180
-181: 3, 11, 19, 25*, 34, 37, 40.
(due 02/27)
3.5 pg. 207 - 208: 3, 4, 10*, 22,
28, 40, 49, 53*.
Additional Homework
Week 03/06 - 03/10
4.1 pg. 251 -
252: 3, 5, 12, 15*, 20, 21*, 26
(due 03/10)
5.1 pg. 297 - 299: 2, 4, 13, 18, 25*, 33
Additional Homework
Week 03/20 - 03/24
5.2
pg. 312 -313: 6, 11*, 30.
Extended: (due 03/27)
5.4 pg. 341-343: 3, 6, 5, 24*, 27, 29.
Additional Homework
Week 03/27 - 03/31
6.1 pg. 375-377:
1-8, use Maple to solve 10, 14, and 17, 24.
14*-phase plane analysis and general solution
(due 04/03)
6.2 pg. 389-391: 5, 8 (use Maple)
5*-phase plane analysis and general solution
6.3 pg. 402-406: 26-34 (ONLY the first part: describe the
interaction of the populations)
Print out the graphs in Maple and attach them to your homework.
Week 04/03 - 04/07 7.1
pg. 444-445:
3,
9*, 13, 16*,
28, 32
(due 04/10)
7.2 pg. 455-456: 4, 13, 19, 23*.
Additional Problem:
Explain in your own words when one can use the Laplace transform to
solve an IVP,
and list all cases when this is not possible. Provide examples in each
case.
Week 04/10 -
04/14 7.3
pg. 465: 5, 15,
18, 30
(due 04/17)
7.4 pg. 474: 5, 8, 16.
Week 11/28 -12/02 7.5 pg.
484-485: 4, 15, 22.
(due 04/24)
7.6 pg. 495-496: 2, 6, 9.
Quizzes:
During the semester there will be up to 10 unannounced
quizzes (5-10 min each) from the sections covered in class. Their
scores will count as bonus points
towards the final grade. A maximum score on a quiz (10 points) is worth
1 point towards the final grade.
Project: There will be one
project assigned in this class on which you may work individually, or
in a group. You may be tested on the
material from the
project on tests and/or on the final exam!
Project
(pdf) - due April 10, 2006 - You may ask questions about the project
until April 6, 2006
Assessment: Your final
grade will be computed based on the follwing scheme.
15 % Project
15% Homework
15 % Exam 1
15 % Exam 2
15 % Exam 3
25 % Final Exam
Bonus Points: up to 10 % from Quizzes
The final letter grade will be computed based on the
following table:
Final average
|
98-100
|
92-98
|
88-92
|
85-88
|
80-85
|
77-80
|
74-77
|
70-74
|
67-70
|
64-67
|
60-64
|
55-60
|
<55
|
Letter grade
|
A+
|
A
|
A-
|
B+
|
B
|
B-
|
C+
|
C
|
C-
|
D+
|
D
|
D-
|
F
|
For borderline cases when the score is within 0.2 from a cutoff grade
(e.g. if the final score is between 79.8 and 80.2), then
the grade will be computed by taking into account other grades in that
range. For example, if there is a cluster of grades
between 78.3 and 80.1 which are separated by .2 or less, all these
students will receive a B-. If there is a cluster of grades
between 79.8 and 83 then all these students will receive a B.
Course Policy:
Class attendance is expected.
If you miss a class it is your responsibility to get
the material
from your colleagues. Make-up exams will be
administered only in extreme cases. Cheating will
be penalized by at best giving a lower letter for the course
grade.
If you have any questions
or suggestions, please feel free to bring them
up!
Announcements:
- On Wednesday, 01/18 class will be held in Avery
Hall 12. Stop by my office before class if you have trouble locating
the room.
- Homework 1 is due on Thursday, January 19 at 9 a.m.
- Class meets in Avery Hall 12 on Monday, February 27.
- Class meets in Avery Hall 12 on Wednesday, March 29.
Exam
1 - Wednesday, February 8 - Review
Problems for Exam 1
(pdf)
Solutions to Review Problems for Exam 1 (.tif)
Problem 37 in 1.5 (.tif)
Substitution Method for an IVP
Exam
2 - Wednesday, March 1 - Review
Problems for Exam 2 (pdf)
Solutions to Review Problems for Exam 2
Exam 3 - Friday,
April 21 - Review
Problems for Exam 3 (pdf)
Solutions to Review
Problems for Exam 3
Additional Problems with Laplace Transform
Formula Sheet for the Laplace Transform
(included on the exam)
Review
for the final exam :
Final Exam - Spring 2005
Differential equations :
- Modeling: natural growth, logistic models,
Newton's Law of cooling,
harmonic oscillators, acceleration-velocity models, tank (mixture)
problems
- First order equations:
-
theorems of existence and uniqueness (linear case)
- separable, linear DE (method of integrating factor), homogeneous,
exact,
reducible second-order
- Euler's Method
- slope fields; phase line analysis
- Second order:
- theorem of existence and uniqueness
- homogeneous: characteristic equation, fundamental solutions
- nonhomgeneous: method of undetermined coefficients, variation of
parameters.
- initial value problems.
- Systems of differential equations:
-modeling (predator-prey, competing, cooperating populations),
connected tanks, etc.
- eigenvectors,
eigenvalues, solving IVPs
-phase plane analysis, stability
- Laplace Transform:
- definition, linearity, the Laplace transform of derivatives, inverse
Laplace, the Heaviside function
- applying the ``shifted transform" formulas, solving DEs and systems
of
DEs with Laplace Transform
- convolutions: definition, the convolution theorem
- Dirac mass: definition, theorem for nonhomogeneous equations
(Duhamel's Principle).
Introduction to some Maple commands
The motion of a spring in Maple
Systems of Differential
Equations in Maple -
exact solutions, plots, eigenvectors and eigenvalues
Euler's Method
for DEs and systems and DEs
Nonlinear Systems -
Phase plane, Trajectories