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Differential Equations (92.236)
Course Description and Requirements

Course Description
This course represents an introduction to mathematical modeling and to the various solution techniques available to solve and analyze the resultant differential equations. The emphasis in this first course in differential equations is on the development of basic skills for the modeling and analysis of physical systems governed by one independent variable (our focus here is on ordinary differential equations - ODEs). Computer implementation for visualization, analytical and numerical solution, and comprehensive analysis is also emphasized. Several computational examples are illustrated using the Matlab package.

The topics discussed follow the textbook by Edwards and Penny quite closely. In particular, our goal is to complete nearly all the material from Chapters 1-4 and Chapter 7 in the text. In addition, extra emphasis is placed on the mathematical modeling of physical systems from basic principles (i.e. basic mass, energy, particle, and force balances, etc.), on the numerical solution to initial value problems (IVPs), and on the implementation, visualization, and analysis of the physical solutions within the Matlab code.

Overall, this course tries to develop a solid mathematical foundation in differential equations and to give the student practical skills for

  • modeling and analyzing physical systems,
  • solving ODEs both analytically and numerically, and
  • working with Matlab to help simulate, visualize, and understand the physical systems under study.

In addition, through class examples and student homework problems, a suite of useful tools for solving a variety of classical problems is developed. These tools and a traditional mathematical foundation in solving ODEs should give the student the necessary prerequisites for more advanced studies in his or her upper-level technical courses.

C. H. Edwards Jr. and D. E. Penny, "Differential Equations and Boundary Value Problems -- Computing and Modeling," 3rd Edition, Prentice Hall, 2004.

Matlab is available in many of the computing labs at the University, so you do not need to buy the software. However, it is a good investment if you have your own PC. The latest student version is “MATLAB & Simulink Student Version Release 14 (with SP3),” The Mathworks, Inc., 2004.

Also, there are many good Matlab texts that are available if you are really interested in learning Matlab (see the website for a detailed list). One book I particularly like is by Amos Gilat, “Matlab: An Introduction with Applications,” 2nd Edition, John Wiley & Sons, 2005. This would be a good place to get started…

Course Website

Course Requirements
The requirements for this course include three exams during the semester and a comprehensive final examination during Finals week. No makeup exams will be given (except for extreme emergency situations) -- any missed exam during the semester will simply be the evaluation dropped from the averaging process (see below).

Homework assignments that include a combination of analytical and computational work are also assigned, collected, and reviewed on a regular basis. Roughly 15-16 assignments will be given over the course of the semester. One or two problems, chosen arbitrarily from each homework set, are formally graded, and this evaluation is used as an important component of the overall course evaluation. Late homework is recorded as being complete, but no numerical grade is given, since some solutions are discussed in class and all solutions are posted on the board outside my office just after the assignments are collected.

Short quizzes may also be given to address key concepts from previous classes and labs. These quizzes will be evaluated and counted as part of the HW Grade for this course.

Usually one or two special projects are also given during the semester. These projects are evaluated as part of your overall HW Grade. The projects typically require a combination of analytical and computer analyses and a professional summary report of your work. The project reports should discuss any required mathematical analysis and identify the key results and conclusions that were obtained. Small groups of 2 or 3 students are encouraged to work together for these projects.

Grading Policy
There are five quantitative measures of your overall performance in this class -- the HW, quizzes, and projects as one composite evaluation, the three exams during the semester, and a comprehensive final exam. Each evaluation is counted as 20% of the final course grade. However, if your Final Exam grade is higher than your lowest evaluation during the semester, it will be used to replace the low grade, effectively making the Final Exam worth 40% of the course grade. If the Final is your lowest evaluation, each individual measure will simply be worth 20%. Note also that, with this scheme, a missed exam during the semester will simply be the score dropped from the final course evaluation.

Thus, the final grade for this course will be determined from a combination of the semester evaluations and the Final Exam, depending upon the quality of your Final, as follows:

"Good" Final Exam
"Poor" Final Exam
Total HW and 3 Regular Exams*
Final Exam

* The lowest grade from this set is dropped if the Final Exam is better than the lowest grade.

Course Coordinator
Dr. John R. White
Office: EB302
Phone: 978-934-3165
Fax: 978-934-3047

Note: My office hours for this semester will be posted outside my office and on my website at during the first week of the semester -- as soon as my schedule becomes finalized.

Last updated by Prof. John R. White (January 2007)

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