Course Information

Course: Math 250, Differential Equations, Spring 2003, Central College.
Professor: Tom Linton, 312 B Central Hall, (641) 628-5264, email: lintont@central.edu.
Class Meets: MWF 2:00 to 2:50 PM in Central Hall 310.
Office Hours: 9 AM Mon, Fri, 1 PM Tues, 3 PM Wed, or by appointment.
Texts: Differential Equations, 2nd Edition, by Blanchard, Devaney, and Hall.
      Differential Equations with Mathematica, 2nd Edition, by Coombes et. al.
Technology: We will make extensive use of the program Mathematica and perhaps other software related to differential equations. No prior knowledge of these tools is assumed. The class web page is located at the URL http://www.central.edu/homepages/lintont/classes/spring03/diffyqframeset.html and information relevant to this course may come via email. You should check your email and the class web page on occasion. We will also use the on-line course management program  Blackboard to distribute and collect materials for this class, as well as post grades for completed assignments.
Final Exam: 1 PM Thursday May 8, Central Hall 310.
Course Overview Differential equations describe how quantities change, and can be used to predict the future values of these quantities. From calculus we know that the rate of change is given by the derivative, thus we will be studying equations involving an unknown function and its derivatives. Many problems in mathematics, engineering and several areas of science lead naturally to such expressions. This introductory course will feature modeling and graphical visualization as central themes, as well as covering the more traditional topics of solving differential equations algebraically.

Goals and Objectives Upon completion of this course, students will:

American Disabilities Act Central College abides by interpretations of the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973 that stipulates no student shall be denied the benefits of an education “solely by reason of a handicap.”  Disabilities covered by law include, but are not limited to, learning disabilities, hearing, sight or mobility impairments, and other health related impairments.  If you have a documented disability that may have some impact on your work in this class and for which you may require accommodations, please see me and Nancy Kroese, Director of Student Support Services and Disability Services Coordinator, (x5247) so that such accommodations may be arranged.
Grades Grades, based on the letter, or A, A-, B+, B, B-, . . . system, will be based on a weighted curve of the total points in the class. The curve used will be the traditional 100-93 A, 92-90 A-, 89-88 B+, etc. (or an easier curve). The breakdown of the points in the class is given below. There is no extra credit for this class. Late assignments (homework, projects, etc.) will be penalized 10% for each lecture day of tardiness, up to the date the assignment is returned (graded). Once I hand back graded versions of an assignment, no points will be rewarded for later versions of that assignment. You are encouraged to work together on group assignments (including homework), but copying answers of others (including those in the back of the text) will result in no credit. Some assignments in this class will be completed on an individual basis (working with others is forbidden). Working together does NOT mean copying someone else's work, in fact, a good rule to always follow is:

When you require help on a problem, you should only have your helper
look at what you have done, and give you advise. You should never look at what they have done.

Exams We will have three midterm exams (100 points each). These exams will most likely follow our completion of chapters 2, 3, and 5. We will also have a cumulative final exam (150 points) on Thursday, May 8 at 1 PM.

Homework, Quizzes, Projects, and Activities I will assign and collect homework problems on a regular basis (one assignment from each section we cover). Recording "just the answer" will receive little or no credit. You should show and/or explain your work on all assignments for this class. You are encouraged to work together on homework assignments, but this does NOT mean copying the work of others nor answers from a solution set. We will do several in-class activities throughout the semester (where new concepts are introduced, or old notions are examined in more detail). Most of these activities will be done in groups, and all will contain questions similar to homework problems. We may have some (4 to 5) quizzes. We will have roughly 350 total points for this portion of your grade.

Mathematica Assignments We will complete 3 to 5 assignments from the supplementary text by Coombes et. al. These will require extensive use of Mathematica and have a value of about 150 points.

Participation You are expected to be in class each day. If you miss a day of class, you are still responsible for the materials-activities completed that day. You are expected to participate in class discussions, ask questions, and to be engaged in the day to day actions of the class. There will be roughly 50 points related to your class participation.

Academic Dishonesty
Plagiarism (which includes working together on an individual assignment, or editing someone else's work and turning it in with your name on it), or copying answers from other people or books without citing the source is a serious offense and will result in no credit for the work and possibly more serious punishment (failing the class, placing a letter in your file, and withdrawl from school are possibilities).  It is OK to discuss your answers with other groups on group assignments, but  the work you turn in must be your own, not a modified version of someone else's work.

Central College's Academic Honesty Policy
"Academic dishonesty is defined as behavior that is inappropriate for academic pursuits, including plagiarizing, cheating and other such dishonest activities.  Some examples of misconduct are

Depending on the nature of the offense, the penalty for academic dishonesty ranges from permission to redo the project (if plagiarism was inadvertent), failing the project, to failing the course.  A second offense is grounds for dismissal from Central College."

Materials As the semester progresses, more links will be added here.
Off Site Links
Hundreds of links to Mathematica related things are located at http://www.wolfram.com.
Be sure to look at http://www.mathSource.
A list of many sites related to Mathematica  http://smc.vnet.net/mathsite.html (not all of which are useful).
Local Activities
The wonderfully powerful Table command.
Looking at Euler's method for numerically approximating solutions with Mathematica.
A quick and dirty look at slope fields in Mathematica.
Problem set B hints and changes, plus a sample write-up of number 12.
A look at bifurcations using Mathematica.
Using Mathematica to help locate bifurcation values.
Using numeric integration in the solution of a linear differential equation.
Using the power of Mathematica's graphics to illustrate the links between a phase portrait for a predator prey system, and graphs of the individual populations as functions of time.


Schedule Relevant information will be added to this schedule as we progress through the semester. An up to date version is available on line at http://www.central.edu/homepages/lintont/classes/spring03/diffyq/index.htm#schedule .
 
BDH = text book, MA = Mathematica Supplement
Week
Dates
Section(s)
Assignment and due date
1 1-13 to 17 BDH 1.1, 1.2
MA chp 1 to 3
 BDH 1.1# 1,3,5,7,13,15,19 due 1-17
BDH 1.2#1,2,7,11,21,25,30,35,37 due 1-27
MA problem set A due 1-20
2
 1-20 to 24
 BDH 1.3
MA chp 4,5
 1.3#3,4,10,14,21,24abd due 1-29
3
 1-27 to 31
 BDH 1.4
MA chp 6
  Euler's method activity
1.4# #2 (by hand), 6,7,8,9,11,13,16
Due Monday 2-3
4
 2-3 to 7
 BDH 1.5
 1.5 #2 (by hand), #6,7,8,9,11,13,16
Due Monday 2-3
5
 2-10 to 14
 BDH 1.6
MA Set B
 1.6 #5,8,17,20,23,24,30,34
Problem Set B # 5,9,10,15
hints-changes, and a sample solution
6
 2-17 to 21
 BDH 1.7,1.8,1.9
 1.7 # 2,3,6,9,10,16ab,24 due Mon 2-17
bifurcations animations,
locating bifurcation values.
1.8 # 2,4,8,9,10,16,24
Using numeric integration inside linear DEs
1.9# 1,2,6,10,11,16,20,24,26
7
 2-25 to 28
 exam 1
  
8
 3-3 to 3-7
 2.1
 2.1 #1,2,4,8,19,22,25,27,28 due 3-19
Due 3-17: Activity for predator prey systems,
phase portraits and standard plots.
 
  
 Spring break!
9
 3-17 to 21
 2.2
 2.2 # 2,4,8,10,11,18,26
10
 3-24 to 28
 2.3, 2.4
 2.3 # 2,3,6,7,8,9,10
2.4 # 2,4*,6*,10
* use Mathematica to print dir field
11
 3-31 to 4-4
  
 exam 2
12
 4-7 to 11
 3.1
 3.1#4,6,8,12,24,26,27
13
 4-14 to16
 3.2
 3.2# 2,6,8,12,16,19,22
14
 4-23 to 25
 3.3
 3.3# 6,10,14,20,23,24 Due Fri 4-25
15
 4-30 to 5-2
 3.4, 3.5
 3.4 #2,4,6,8,10,12,14
3.5 #2,6,11,22
17 May 8 1 PM  Cumulative final exam