# Math 252-01 Spring 2002

Special information for Prof. Bumby's section will appear on this page. (Use link in previous sentence for office hours and other information on contacting the instructor.) Common features of all sections appear on the semester page. Students are encouraged to explore the Information and Resources links on the course history page

## Schedule of quizzes, projects and exams

• Thursday, January 31: Quiz on 1.1 (modeling) and 1.2 (separable equations).
• Thursday, February 07: Quiz on 1.2 (separable equations) and 1.3 (slope fields)
• Thursday, February 14: Quiz on 1.6 (the phase line) and 1.7 (bifurcations)
• Project 1 is due on February 25. A printed version of this project description was distributed in class on February 11. Some things that you might have included in the project are described in a answer guide. Note that this document has a password that will be given to anyone who has submitted the project., Also, it is for viewing only; it cannot be copied or printed, but it may still be useful when reviewing work on the project and preparing for other projects.
• Monday, March 04: Tentative date for first exam. This is the twelfth meeting, so is the time suggested on the standard syllabus. The exam will cover chapter 1 and the first two sections of chapter 2, including those supplementary notes prepared to clarify the Rutgers view of that part of the textbook.
• Thursday, March 28: Quiz on 3.1 through 3.4 (matrix exponentials of two-by-two matrices applied to differential equations)
• Project 2 is due on April 11. A printed version of this project description was distributed in class on March 25. A connection to biology, mentioned briefly in the introduction can be found in chapter 24 of "Modeling Differential Equations in Biology" by Clifford Henry Taubes, published by Prentice Hall, 2001 (ISBN 0-13-017325-8). A different system is used in that book, but the second order equation for x is the same (except for the presence of an extra parameter, denoted by epsilon, in the book).
• Monday, April 15: Tentative date for second exam. The exam will cover chapter 3.
• Monday, April 22 and Thursday, April 25: Start of digression into Sections 5.2 and 5.3. Suggested homework from 5.2: 1, 7, 9, 11. Suggested homework from 5.3: 1, 3, 13.
• Monday, April 29: Quiz on 5.1 and 5.2.
• Monday, May 06: Last class. Topics from sections 8.3 and 8.4 will be used to illustrate why the beginning of chapter 8 was included in the course.
• Friday, May 10, noon to 3PM: final exam in the regular classroom (SEC-212). The exam questions will be one a paper that you can keep with answers to be written in blue books. It is a closed book exam, but you may use and will need a calculator.

## Supplementary Material

• N1 Most recent revision (Spring 2000) of modeling notes.
• Example from Section 1.2 in a Maple worksheet. (Shift-click to save, then load it into Maple.)
• Examples from Section 1.3 shown in lecture on January 31 in a Maple worksheet. (Shift-click to save, then load it into Maple. Graphs will be drawn on separate pages.)
• The Euler's method notes from Spring 2000 discuss numerical methods and their role in a proof of a form of the existence and uniqueness theorem for initial value problems.
• Here is the course overview with review problems that was distributed at the last class.
• In response to a question immediately after the end of the last class, a printed report has been prepared to show the use of Maple to provide details of the example from section 5.2 that was similar to the colorful quiz problem.

This section was unused during the semester, but it is an ideal place for a report on the final exam and course grades. The figure below compares the final exam with the total of all classwork. Grades were based on clusters in the sum of these two scores, but this plot helped to interpret those totals by providing a graphical view of the components.

The avearage score on the final exam was 136.64 out of 200. Most of the grades were between 138 and 155. Seven grades were in this range. There were only two higher grades, but five lower grades. Here are details of individual problems (using a scaled average that gives each problem a basis of 10 points.

Prob. # Scaled Avg.
1 6.79
2 7.46
3 6.18
4 7.64
5 8.21
6 5.89
7 7.03
8 5.51
9 7.20

The course grades were: 1 A, 4 B+, 4 B, 2 C+, 3 C. There were three other names on the roster, but these students stopped attending class before the final exam.