Mathematics 254
Introduction to Ordinary
Differential Equations
Summer I 2016
Course Home Page
Overview.
In Introduction
to Ordinary Differential Equations, we shall be using your background in
science and engineering and your previous knowledge of algebra and calculus to
consider the practical questions in ordinary differential equations. In single
variable calculus, we use techniques of integrations that allow us to determine
yÕ(x) = f(x) with
y(a) = c
by
integration.
The term ordinary
indicates that we will be consider y
along with its derivatives yÕ,
yÕÕ, É as functions
of a single variable x. We
can write this differential equation as
F(x, y(x) , yÕ(x)
, yÕÕ(x), É , y(n)(x)) = 0.
The highest derivative in this expression, n, is called the order of the differential equation. Ordinary differential equations are used to
model and analyze any situation in which the change in some function depends on
the value of the function. These models can be seen in mechanical motion,
dynamical properties of electrical circuits (physics), the motion of celestial
bodies (astronomy), chemical reactions (chemistry), changes in land forms
(geology), heat transfer and thermodynamics (mechanical engineering),
properties of materials (material science and optics), population models
(ecology and epidemiology), and the flow of capital and goods (economics)
Day-to-Day Operations.
The class meets daily from 11:00 AM to 12:45
PM in room 210 of Biological
Sciences West Building . The textbook is Fundamentals of Differential
Equations (Eighth Edition) by R. Nagle, E. Saff, and
A. Snider. The course will cover
the majority of chapters 1, 2, 4, 5, 8, and 9. The exact schedule of topics and
assignments are given in the course syllabus.
With the intensity of a summer session course
and the need to develop solutions techniques and strategies for interpretation
of the solutions to ordinary differential equations, we will hold office hours
and problem sessions in the Slot Canyon CafŽ inside the Environmental and Natural
Resources Building 2 both before and after class.
Feel free to stop by my office in room S321 of
the Environmental and Natural
Resources 2 Building, call me at 621-5245 or send an email to jwatkins at
math.arizona.edu or through d2l.arizona.edu
Evaluation
of Students.
Students will be evaluated through
homework exercises, group projects, and exams. Homework will be due
approximately 2 to 3 times per week. Group projects will generally completed in
groups of two. They are described at the end of each chapter of the textbook.
The grading scheme is
|
number |
points |
total |
|
|
calculus pre-test homework |
1 10 |
50 10 |
50 100 |
|
projects |
5 |
20 |
100 |
|
midterm exam |
2 |
100 |
200 |
|
final exam |
1 |
150 |
150 |
|
total |
600 |
Grades will be given on the usual scale A is 90%-100%, B is
80%-89%, C is 70%-79%, D is 60%-69%, and E is below 60%. The instructors may move these cutoff values down.
Any grading disputes must be addressed within one week after an exam or
homework has been returned. If you fail to complete the course due to
circumstances unforeseen, then you may qualify for a grade of I, ÒincompleteÓ
in accordance with University Policy.
Students should take the time to become familiar with policies and codes
of the University, notably the academic
integrity policy and student
code of conduct. Student with special needs should contact SALT - Strategic Alternative Learning
Techniques Center or the Disability
Resources Center.
Best wishes to you for a good summer in this course and in
all your other activities.
- Joe Watkins