I. MTH 238 Applied Differential Equations I - 3
Semester Hours
II. Course Description
An introduction to numerical methods , qualitative behavior of first order
differential
equations, techniques for solving separable and linear equations analytically,
and
applications to various models (e.g. populations, motion, chemical mixtures,
etc.);
techniques for solving higher order linear differential equations with constant
coefficients
(general theory, unde termined coefficients , reduction of order and the method of
variation of parameters), with emphasis on inter preting the behavior of the
solutions, and
applications to physical models whose governing equations are of higher order;
the
Laplace transform as a tool for the solution of initial value problems whose
inhomogenous terms are discontinous.
III. Co-requisite
MTH - 227
IV. Textbook
Due to the varied selection of quality college level textbooks, each college
will select the
textbook needed to meet the requirements of this course.
V. Course Objectives
The objective of this course is to provide an introduction to differential
equations for the
pre-engineering major as well as the mathematics major whose curriculum requires
a
course in ordinary differential equations. The course is de signed for
pre -engineers who
need applications of differential equations. However, the development of the
theory
necessary to justify the applied problems is sufficient for the mathematics
major. This
course will provide the necessary background for future studies in the “theory”
of
differential equations if necessary.
VI. Course Outline of Topics
A. This course shall include the fol lowing topics as a minimum.
1. Definitions and termino logy , initial – value problems
2. Differential equations as models
3. Separable variables
4. Exact equations
5. Linear equations
6. Solutions by substitutions
7. Linear equations
8. Nonlinear equations
9. Systems of linear and nonlinear equations
10. Linear equations and boundary value problems
11. Introduction: homogenous and nonhomogenous equations
12. Reduction of order
13. Homogenous linear equations with constant coefficients
14. Undetermined coefficients
15. Variation of parameters
16. Cauchy – Euler equation
17. Systems of linear equations
18. Nonlinear equations
19. Spring / Mass systems
20. Linear equations: boundary value problems
21. Nonlinear equations
22. Power series solutions
23. Solutions about ordinary points
24. Solutions about singular points
25. Laplace Transform
26. Applications of Laplace Transforms
27. Dirac Delta Function
VII. Evaluation and Assessment
Evaluation and assessment techniques may include any or all of the following.
Exams
Projects
Homework
Computer activities
Class participation
Grades will be given based upon
A = 90 – 100%,
B = 80 – 89%,
C = 70 – 79%,
D = 60 –69%,
and F = below 60%.
VIII. Attendance
Students are expected to attend all classes for which they are registered.
Students who are
unable to attend class regularly, regardless of the reason or circumstance,
should
with draw from that class before poor attendance interferes with the student’s
ability to
achieve the objectives required in the course. Withdrawal from class can affect
eligibility
for federal financial aid.
IX. Statement on Discrimination/Harassment
The College and the Alabama State Board of Education are committed to providing
both
employment and educational environments free of harassment or discrimination
related to
an in dividual ’s race, color, gender, religion, national origin, age, or
disability. Such
harassment is a violation of State Board of Education policy. Any practice or
behavior
that constitutes harassment or discrimination will not be tolerated.
X. Americans with Disabilities
The Rehabilitation Act of 1973 (Section 504) and the Americans with Disabilities
Act of
1990 state that qualified students with disabilities who meet the essential
functions and
academic requirements are entitled to reasonable accommodations. It is the
student’s
responsibility to provide appropriate disability documentation to the College.
