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:

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