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Course Description and Requirements
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
and analyzing physical systems,
ODEs both analytically and numerically, and
with Matlab to help simulate, visualize, and understand the
physical systems under study.
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
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 mathworks.com
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…
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.
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:
HW and 3 Regular Exams*
The lowest grade from this set is dropped if the Final Exam is
better than the lowest grade.
Dr. John R. White
My office hours for this semester will be posted outside my office
and on my website at profjrwhite.com
during the first week of the semester -- as soon as my schedule
updated by Prof. John R. White (January 2007)
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