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Ordinary Differential Equations
Course Description:
This course is an introduction to the subject of differential equations and
has three
components:
1. Existence theory and classical methods for first order equations
(chapters 1&2)
2. Real life applications and the theory of linear equations (chapters
3&5)
3. Techniques and methods for solving general linear equations: operator
method ,
power series , and an introduction to the Laplace transform (chapters 4, 6&7).
We shall use the computer algebra system Maple for symbolic computations and for
its
linear algebra and integral transforms packages.
Learning Outcomes: the student will be able:
To identify and classify differential equations
To decide whether a solution is unique and find its domain of existence
To solve first order equations by classical methods
To model a simple process and determine its evolution for large time
To solve an inhomogeneous equation using undetermined coefficients or variation
of
parameters
To find power series solutions of linear equations with analytic coefficients
To use transform methods to solve linear differential equations
To use computer resources to solve ordinary differential equations symbolically
Tests and Final Exam:
There will be two in class tests and two takehome tests worth 100 points each.
Takehome
tests are supposed to be completed individually. The lowest of these test scores
will
be dropped. You can miss at most one test, and that test will be considered to
be the test
with the lowest score to be dropped. The final counts 200 points. No makeup for
missing
tests and final exam.
9/12 : Test 1 (Takehome), due 9/14
10/19 : Test 2 (Inclass)
11/7 : Test 3 (Takehome), due 11/9
11/30 : Test 4 (Inclass)
12/12 : Final 810AM
Grading: The final letter grade will be determined by the following
scale:
A = 450500, B = 400449, C = 350399, D = 300349, F = below 300
W Deadline: October 8^{th} is the last day to withdraw with grade of W
Homework: This is an important part of the course.
At the end of most classes you will
be given a list of problems – these are the minimum that you should work on.
These
problems will not be graded. Some of these problems will be gone over in the
next class
session and some will be included into the inclass tests. Practice is
important. I
encourage you to use my office hours if you have any question about them. You
should
make sure to set aside some time every day to work problems.
Disabilities: Students with documented disabilities
(through West Georgia’s Disability
Services) will be given all reasonable accommodations. Students must take the
responsibility to make their disability known and request academic adjustments
or
auxiliary aids. Adjustments needed in relation to testtaking must be brought to
the
instructor's attention well in advance of the test (at least one week prior).
Attendance Policy: You are expected to attend every
class. Although absences are not
penalized, if a class is missed, you are responsible for all material and
assignments.
Academic Honesty: You are expected to achieve and
maintain the highest standards of
academic honesty and excellence as described in the Undergraduate Catalog. In
short, be
responsible and do your own work.
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