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

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.Text: C. Henry Edwards and David E. Penney. Differential Equations : Computing and Modeling, 3rd Edition, Pearson Education, Inc.

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:

- By turning in ALL the homework that is assigned above at the end of the semester (5 points added to your final score). No partial credit given.
- By taking bonus quizzes during the semester (each quiz is worth half a point towards the final score).
- By attending Sir Michael Atyiah's lecture "The Nature
of Space", Friday, October 21 in
Kimball Recital Hall at 4:00 pm and answering a
mathematical question related to his talk (2 points towards the final
grade). More details will be given in class before the lecture.

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!

- On Tuesday 08/30/2005 the class will be held in Avery Hall 12. Stop by my office before class if you have trouble locating the room.

- A Forum was created on the blackboard web site for this class. If you login on the site www.my.unl.edu and click on the link for this course you will find the 221 Forum under the Communication link.

- I created 5 mailing lists, one for each study group. Please make sure that you receive e-mail from the study group you signed up for. If you want to ask a question in your study group, just send an e-mail to the corresponding study group:

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:

- On Thursday 10/06 class
will be held in Avery Hall 12.

- Starting
next week (10/04) ALL homework problems will be collected; however, only the problems
marked by an asterisk will be graded, the rest of the problems will
count towards bonus points. Also, the homeworks from Chapters 1 and 2
can be turned in, so by the end of the semester the entire homework
assigned during the semester will count as bonus credit. Note that you need to turn in ALL your
homework in order to obtain all 5 bonus points towards the final grade,
as no partial credit is given for partial homework.

- On Tuesday 10/25 class will be held in
Avery Hall 12.

- If you were not able to get in for Sir Atiyah's talk, you may get the extra credit (2 points) by writing an one to two page report on your favorite mathematician (focus on mathematical statements, rather on facts about his/her personal life).
- The third exam is tentatively scheduled for Tuesday, November 22 (before Thanksgiving). Please announce me, if this conflicts with travel plans that you may already have made.
- If you are missing only one or two problems from the homework (which is not graded), stop by my office to discuss them with me and give oral solutions.
- WUMN (Women's Undergraduate Math Network) has a game night +
free food tonight (10/25) between 5:30 and 6:30 in the undergraduate
lounge on the third floor in Avery Hall. Everyone is invited!

Introduction to some Maple commands

The motion of a spring in Maple

Systems of Differential Equations in Maple - exact solutions, plots, eigenvectors and eigenvalues