Math 221-- Differential Equations
Sections 004 and 006

Spring 2005


Instructor:   Petronela Radu
                    Office: AVH 239
                    Phone: 472-9130
                    E-mail: pradu@math.unl.edu
Office Hours:   2:30 - 4:00 pm Tuesday & Thursday
                           or by appointment

Schedule of classes: 


Section 004: 11:00-12:15 Tuesday & Thursday ---- Avery Hall 118
Section 006: 12:30-1:45  Tuesday & Thursday ---- Oldfather Hall 204

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 during final examination week (May 2—6).

 
Section 004: 10:00-12:00 Thursday, May 5 ---- Avery Hall 118
 
Section 006: 1:00 - 3:00     Monday, May 2 ---- Oldfather Hall 204
  You must arrange your personal schedule to permit you to take the final exam at the regularly scheduled time. 
 
Computer Lab / Calculators: Students will be given an account in the Mathematics Department Computer Laboratory in Avery 18. In this section of the course, the use of a computer algebra system is not required, but it is 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.
 
Syllabus: You can find here a copy of a tentative syllabus. Please disregard any mention to the second project which will not be assigned in this section of the course.

Daily Work: The homework will be announced in class and posted on the web site every week. The homework will not be collected, but you will be tested on the material taught in class through quizzes.

Homework:
Week  01/10 - 01/15           1.1 pg. 8-9:  3, 9, 16, 22, 25, 30, 35
                                         1.2 pg. 16-18: 3, 6, 10, 14, 22, 25, 30
                                         1.3 pg. 26-29: 2, 8, 12, 15, 21, 27 

Week 01/17 - 01/22           1.4 pg. 41-44:  5, 10, 16, 17, 24, 31, 35, 38, 49, 61
                                        1.5 pg. 54-56: 3, 9, 16, 22, 30, 33, 37

Week 01/24 - 01/28           1.6 pg. 71-72:   7, 14, 29, 37, 47
                                        2.1 pg. 86-88:   7, 9, 18, 21,  24
                                        2.2 pg. 96-97:   6, 10, 20, 21

Week 01/31 - 02/04           2.3 pg.  106-107:  1, 2, 4,  13,  14, 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 02/14 - 02/21           3.1 pg. 155 -157: 3, 6, 9, 16, 18, 20, 22, 27, 33, 37, 40
                                        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 02/28 - 03/04           3.3 pg. 180 -181: 3, 7, 18, 19, 23, 26, 34, 37, 40, 43, 44.
                                        3.5 pg. 207 - 208: 3, 4, 5, 10, 13, 22, 28, 31, 40, 43, 49, 53.
 
 Week 03/21 - 03/25           4.1 pg. 251 - 252: 3, 5, 11, 12, 14, 19, 21, 26
                                         5.1 pg. 297 - 299: 2, 4, 6, 12, 18, 21, 24.
                                     
 Week 03/28 - 04/01           5.2 pg. 312  -313: 2, 5, 10, 29, 38.
                                         5.4 pg. 341-343:  2, 4, 6, 23, 27, 30
                                         6.1 pg. 375-377: 1-8, 13, 15, 16, 19, 20, 23.  

Week 04/04 - 04/08            6.2 pg. 389-391: 1, 3, 7, 9
                                         6.3 pg. 402-406:  26-34 (ONLY the first part: describe
                                                                   the types of populations and the nature of their interaction)

Homework assignments that will replace quizzes 8, 9 and 10:

Homework 1 (due 04/19/2005):  7.1 pg. 444-445:  1, 8, 19, 21, 29, 32.
Homework 2 (due 04/21/2005):  7.2 pg. 455-456:  5, 15, 18, 20.
Homework 3 (due 04/26/2005):  7.3 pg. 465: 6, 12, 17, 30
                                                7.4 pg. 474: 8, 15
                                                7.5 pg. 484-485: 16, 26
                                                7.6 pg. 495-496: 2, 7.

Announcements:

Final Review Session : Tuesday, 04/26/2005:  7 pm - 10 pm - Teacher's College Hall- room 105.

For Tuesday 04/26 - section 004 (11:00 am) -
class will be held in Military and Naval Sciences (14 th and Vine) - room B5, at the same time (11:00 am).


Material for the final review will cover the following subjects:

Modelling - for differential equations: natural growth, logistic model, Newton's Law of cooloing,
                                                        harmonic oscillators, acceleration-velocity models ...
                - for systems
of differential equations: population models, connected springs, connected tanks ...

Solutions: for equations:
                        first order:
                                     - 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.
                       for systems: 
                                    - theorem of existence and uniqueness for linear systems
                                    - method of elimination
                                    - characteristic equation, eigenvalues, eigenvectors, generalized eigenvectors
                                    - fundamental solutions and initial value problems.

Qualitative analysis:  - slope field and phase line analysis, stability for DE
                                - direction field, nullclines, line trajectories, stability for systems
 
Laplace Transform: definition, properties, inverse Laplace Transform
                            - Heaviside function, piecewise continuous functions
                            - convolution, delta function
                            - solving equations and systems with Laplace Transform.


Quizzes:  During the semester there will be 10 -15 unannounced quizzes (10-15 min each) from the sections covered in class. Their scores will count towards the final grade.

Project: There will be one project assigned in this class on which you may work individually, or in a group. Nonetheless, you will have to write up your own project. You may be tested on the material from the project on Test 2 and/or on the final exam!

Assessment: 
Your final grade will be computed based on the follwing scheme.
                        10 % Quizzes
                       
10 % Project 
                        20 % Exam 1
                        20 % Exam 2 
                        20 % Exam 3
                        20 % Final Exam

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 or quizzes 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 - February 10, 2005 - Review Problems for Exam 1 (pdf)
Exam 2 - March 10, 2005 - Review Problems for Exam 2 (pdf)
                                         Solutions to Review Problems 2 (pdf)
             - Solutions to Exam 2 (tif file -you can open it on a Windows machine)
Exam 3 - April 12, 2005 - Review Problems for Exam 3
                                       Solutions to Review Problems for Exam 3
           
- Solutions to Exam 3 (tif file -you can open it on a Windows machine)
Extra Credit Homework Assignment (graphics) (.pdf) (.ps) - Due April 19, 2005

Introduction to some Maple commands
The motion of a spring in Maple