Welcome to the Math 221H (Honors Differential Equations) home page. You're probably here for information, so let's start with the vital statistics of the course.

### Differential Equation Course Resources

As you know, a staggering amount of information can be found on the web. Of course, some of it helps, some confuses, and some is downright wrong -- caveat emptor! Go to your favorite search engine and try searching on "ordinary differential equation". See how many web pages you hit and visit a few interesting looking sites.

## Notes and FAQ

8/12/08:(Just to get the FAQ started) About significant digits...
I've been asked to explain what "significant digits of an approximation" to a (nonzero) number means. There are several interpretations that one commonly sees. The "absolute" definition, which is perhaps more intuitive, goes as follows: to get the number of significant digits, first *subtract* (rather than just looking at the numbers) the two (may as well be larger - smaller), then find the position of the leading digit of the error relative to the position of leading digit of the exact answer. If the difference in that position is less than 5, then number of significant digits is one less than the difference, else two less.

For example if 3.14 and 3.15 are used to approximate 3.14159, calculate 3.14159 - 3.14 = 0.00159 and 3.15 - 3.14159 = 0.00841. Notice I put a zero in front of the decimal to start counting from the right position. There is a nonzero digit at the 4th position with each approximation, counting from the (base 10) position of the leading digit of 3.14159. The size of this digit is at most 5 in the first case, so this approximation has 3 significant digits. In the second case, the digit is larger than 5, so the approximation only has 2 significant digits.

The "relative" definition is usually preferred in numerical analysis and it goes as follows: if xapprox is used to approximate xtrue, the number of significant digits is largest integer n such that the relative error, |(xapprox-xtrue)/xtrue)| is no larger than 5x10^(-n-1). In our previous example the relevant quotients are 0.000506 and 0.002677, respectively. The best bound in both cases is 5x10^(-3). Thus, this definition will give only 2 significant digits in both cases. In general, the "relative" definition is stingier than the "absolute" one. Hope this helps.

Where do I stand right now?...

Well, that's easy enough. Here's a table to help you out. This table has all the possible grades for tests and quizzes in this course. Notice there are blanks where an activity has not been completed yet. So if you are looking at this table and we've only done the exams through three, then the grade scales are based on this data alone.
Now all you need is your own scores. If you don't have them or simply want to see what grades I have recorded for you so far, email me from Blackboard. I will respond with the grades I have in my grade book. If you calculate your own grade remember that the quiz scale is dynamic and will vary with the number of quizzes currently finished in the course, and that the lowest quiz is dropped. Also note that the grade scales row gives the bottom score to attain the given grade.

### Grade Scales for Math 221, Section 006, Fall 2008

Activity: Quizzes/Writing Exam 1 Exam 2 Exam 3 Final Exam Grade
Points: 150 100 100 100 200 650
Count: 24 24 23 22 22 23
Minimum: 18 50 73 65 124 86
Maximum: 140 97 100 98 200 621
Average: 113 82 92 89 176 527
StdDev: 27 13 8 8 22 126
Median: 121 85 93 92 186 572
D- 36 45 45 45 100 303
D 40 50 50 50 110 335
D+ 42 53 53 53 117 356
C- 45 56 56 56 124 376
C 48 60 60 60 130 400
C+ 52 65 65 65 140 433
B- 56 70 70 70 150 465
B 60 75 75 75 160 498
B+ 63 79 79 79 167 523
A- 66 83 83 83 174 548
A 69 86 86 83 180 567
A+ 74 93 93 93 190 613

Class Policy

Course:Math 221H, Honors Differential Equations

Places/Times: AvH 118, 9:30-10:45 TR, Fall 2008

Preq: Math 208 or 107H or equivalent with a grade of 'P' or 'C' or better, and invitation.

Objectives: The goals of this course are to help students achieve competence in the following areas:

• Mechanics of finding exact solutions to differential equations.
• Forumlation of differential equations as physical models.
• Interpretation of solutions to differential equation models.
• Use of computational tools for solving differential equations.
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233 Home 489-0560

Email: tshores1@math.unl.edu

Office Hours: Monday 2:00-4:00, Tuesday 13:00-15:00, Thursday 11:00-13:00, Friday 9:00-10:30, and by appointment. Office: 229 AvH AvH
Note: Circumstances may necessitate occassional changes in office hours. Consult the course home page for the most current times.

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor. There will be no makeup exams or quizzes.

Homework/Projects: Everyone is expected to master the syllabus homework assignments. These will generally not be graded, but at least one question on each exam and most quiz questions will come directly from these problems. Therefore, students are strongly encouraged to work them and ask questions about them in and outside of class. Current information about the course will be available through the web (via the Math221H homepage in Blackboard or my home page.) Using the web is strongly recommended for keeping track of current activities and resources for the course.

Reading Assignment: Read the sections of the text as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade:Three class exams will be given as specified in the syllabus and these will account for 100 points each. The final exam will count 200 points. All exams are closed book with no calculators. There will be six fifteen minute quizes/assignments at 20 points each, of which the lowest score will be dropped and projects worth 50 points. The dates of the quizzes/assignments will be announced in class one week in advance. The final grade will be based on these 650 points.

Final Exam: Will be comprehensive. To be given on Monday, December 15, 10:00-12:00 noon in AvH 118.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)