Math 221-- Differential Equations

Fall 2005                               
Section 005
Instructor:   Petronela Radu
                    Office: AVH 239
                    Phone: 472-9130
                    E-mail: pradu@math.unl.edu
Office Hours:   2:30 - 4:00 pm Mondays and Wednesdays or by appointment
Schedule of classes:  12:30-1:45  Tuesdays and Thursdays ---- Avery Hall 118
Text: C. Henry Edwards and David E. Penney. Differential Equations : Computing and Modeling, 3rd Edition,  Pearson  Education, Inc.
Final Exam: A comprehensive final examination will be given on Tuesday, December 13,  at 1:00-3:00 pm ---- Avery Hall 118.
   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, the use of a computer algebra system is not required, but it is strongly encouraged for gaining more insight into the material. Student versions of CAS (MATLAB, 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.
Calculators will be allowed during the exams, however the use of any other electronic device (cell phones, ear pieces etc.) will not be permitted.
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. Only one or two problems
(which will be marked by an asterisk *) from the homework will be collected and graded. Each week the homework is worth 10 points. The best 10 scores from the homework assignment will count towards the final grade.

Homework Problems (Solutions to the asterisk problems will be posted after the assignment is due):

Week  08/22 - 08/26           1.1 pg. 8-9:  2, 7, 15, 23, 26, 30, 35  
           (due 08/30)             1.2 pg. 16-18: 5, 7, 10, 16, 20, 26,  30*

Week 08/29 - 09/02            1.3 pg. 26-29: 3, 5, 13, 16, 21
          (due 09/06)              1.4 pg. 41-44: 5, 10, 16, 17, 24, 31, 35*, 38, 49, 61
                                         1.5 pg. 54-56: 3, 11, 16, 21, 30, 33*, 37
                                         Solution   

Week 09/05 - 09/09           1.6 pg. 71-72:   7, 14, 29, 37*, 47
         (due 09/13)              2.1 pg. 86-88:   7, 9, 18, 21, 24
                                        2.2 pg. 96-97:   6, 10*, 20, 21

                                                   Solution  
 
Week 09/12 -09/16           
2.3 pg.  106-107:  1, 2, 4,  13,  14, 20*
         (due 09/20)              2.4 pg.  119-120:  5, 8, 30*.
                                                                   Find the exact solution and the required approximation in 12, 14, 16.
                                                                   Find the approximation for h=.02 in 19, 22, 23.    

Week 09/26 - 09/30          3.1 pg
. 155 -157: 3, 6, 9, 16, 18, 20, 22, 27, 33, 37, 40, 52*
     (due 10/04)                 3.2 pg. 167 -169: 3, 5, 8, 12, 14, 18, 21, 24, 26*, 39
                                       Solutions to 12 pg. 167 and 16 pg. 168. (.pdf)
                                    
Week 10/03 - 10/07         3.3 pg. 180 -181: 3, 7, 18, 19, 23, 26, 34, 37, 38*, 40.

     (due 10/11)                     3.5 pg. 207 - 208: 3, 4, 5, 10*, 13, 22, 28, 31, 40, 43, 49, 53*.

Week 10/10 - 10/14        Tuesday:  Review for Exam 2
                                     Thursday:  Exam 2

Week 10/17 - 10/21         4.1 pg. 251 - 252: 3, 5, 11, 12, 14, 19, 21, 26*
   (due 10/25)                  5.1 pg. 297 - 299: 2, 4, 6, 12, 18, 21, 25, 34*.

                                              
Week 10/24 -10/28          5.2 pg. 312  -313: 3, 5, 10, 29*, 38.
  (due 11/01)                   5.4 pg. 341-343:  2, 4, 5, 23, 27, 30*.

Week 11/01 - 11/04        6.1 pg. 375-377: 1-8, 13, 15, 16, 19*, 20, 23
  (due 11/08)                 
6.2 pg. 389-391: 1, 3, 7, 9*
                                     6.3 pg. 402-406:  26-34 (ONLY the first part: describe the interaction of the populations)

Week 11/07 -11/11        7.1 pg. 444-445:  1, 3, 8*, 16, 19, 21, 29, 32
  (due 11/17)                
7.2 pg. 455-456:  5, 15, 18*, 20*.

Week 11/14 -11/18       
7.3 pg. 465: 6, 14*, 17, 31*
                                   
7.4 pg. 474: 8, 15*
  (due 12/01)                 Review Exam 3
 
Week 11/21 -11/25        Exam 3
                                    Thanksgiving Break

Week 11/28 -12/02        7.5 pg. 484-485: 7, 16, 26*
  (due 12/08)                 7.6 pg. 495-496: 3, 5, 8*.

 
Week 12/05 -12/09     Review for the Final
                                 Tuesday:  Differential equations :
                                      - Modeling: natural growth, logistic models, Newton's Law of cooling,
                                                        harmonic oscillators, acceleration-velocity models, tank (mixture) problems

                                      - First order equations:
                                                  - two theorems of existence and uniqueness (linear and nonlinear case)
                                                  - separable, linear DE (method of integrating factor), homogeneous, exact,
                                                    reducible second-order
                                                 - Euler's Method
                                      - Second order:

                                                  - theorem of existence and uniqueness

                                                  - homogeneous: characteristic equation, fundamental solutions
                                                  - nonhomgeneous: method of undetermined coefficients, variation of parameters.
                                                  - initial value problems.

                                          Thursday: - 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,
                                                       -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.
                                                                                                           
Projects: There will be two projects assigned in this class on which you will work in groups of 3 or 4. You can view the projects as multi-step homework assignments, where you will have to come up with your own solutions and interpretations of the problem. Original/intersting remarks made in your work will receive extra-credit. You may be tested on the material from the projects on the exams during the semester and/or on the final exam!
Assessment:  Your final grade will be computed based on the follwing scheme.
                        10 % Homeworks
                       
10 % Project 1
                        10 % Project 2

                        15 % Exam 1
                        15 % Exam 2 
                        15 % Exam 3
                        25 % Final Exam
The final letter grade will be computed based on the following table:

Final average
98-100
91-97
88-91
85-87
80-84
77-79
74-76
70-73
67-69
64-66
60-63
55-59
<55
Letter grade
A+
A
A-
B+
B
B-
C+
C
C-
D+
D
D-
F

However, depending on the performance of the entire class, your grade may be better than the grade indicated above.

Bonus Points:
       You may earn bonus points during the semester in the following way:


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!

Exam 1 - Thursday, September 22 - Review Problems for Exam 1 (pdf)

Substitution Method for an IVP

Exam 2 - Thursday, October 13 - Review Problems for Exam 2 (pdf)

Solutions to Review Problems for Exam 2 (pdf)

Exam 3 - Tuesday, November 22 - Review Problems for Exam 3 (pdf)
Solutions to Review Problems for Exam 3 (pdf)

Announcements!
       m221-mon@math.unl.edu (the group meets on Mondays)        m221-tue@math.unl.edu (the group meets on Tuesdays)    
       m221-wed@math.unl.edu
(the group meets on Wednesdays)    m221-thu@math.unl.edu (the group meets on Thursdays)
       m221-fri@math.unl.edu
  (the group meets on Fridays or at other flexible times)

09/29:
10/24:
10/25:

Introduction to some Maple commands
The motion of a spring in Maple
Systems of Differential Equations in Maple - exact solutions, plots, eigenvectors and eigenvalues