I. MTH 238 Applied Differential Equations I - 3
Semester Hours
Core Area III, AMTH A116 TMTH (Lec 3 hrs)
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 interpreting 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. Prerequisite
C or higher in MTH 126.
IV. Co-requisite
MTH - 227
V. Textbook
First Course in Differential Equations With Modeling
Applications, Zill, 9th Ed.
Thompson Brooks/Cole, 2009
VI. 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 designed 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.
VII. Course Outline of Topics
A. This course shall include the following 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
VIII. Evaluation and Assessment
A. College requirements:
Examinations should be given by instructors periodically throughout their
courses.
Faculty are encouraged to give evaluative work early in the term so that
students will
have a clear understanding of the progress they are making. Final examinations
will
be given in all classes, and all students enrolled for academic credit will take
the final
examination. (College Handbook, section 3.7)
B. Grading system as stated in the college catalog:
*A - Excellent (90-100)
*B - Good (80-89)
*C - Average (70-79)
D – Poor (60-69)
F – Failure (below 60)
W - Withdrawal (before midterm)
WP - With drawal passing (after midterm)
WF - Withdrawal failure (after midterm)
I - Incomplete
AU - Audit
RW - Required withdrawal
*Satisfactory grades
C. Criteria for evaluation:
1. Recitation
2. Daily assignments
3. Written assignments
4. To receive a grade of “C” or higher, the student must obtain an average of at
least
70% on written test(s) and other evaluation criteria as determined by the
instructor.
IX. Class Activities
A. Lecture
B. Discussion
C. Class participation
D. Written examination
X. General Course Competencies
A. The student will acquire knowledge of families of curves.
B. The student will be able to apply knowledge of the methods presented in this
course
to find the solution of various types of differential equations.
C. The student will analyze various kinds of “ real -world” models from science
and
engineering by using the methods of solving differential equations.
XI. Course Objectives Stated In Performance Terms
A. The student will demonstrate knowledge of families of curves by
his/her ability to
1. eliminate arbitrary constants to obtain the differential
equation of a family of curves.
2. sketch several representative members of a given family.
B. The student will demonstrate knowledge of the methods presented in
this course by his/her ability to
1. use, when appropriate, the following solution techniques for
first-order equations:
a. separation of variables
b. exact equations
c. integrating factors
d. linear equations
e. homogeneous equations
2. solve certain linear differential equations of higher-order:
a. homogeneous linear equations with constant coefficients
b. constructing a second solution from a known solution
c. using the methods of undetermined coefficients and variation of
parameter on the appropriate nonhomogeneous linear equation
3. use the Laplace transform to solve a given initial valve problem.
4. obtain power series solutions of certain differential equations
with variable coefficients :
a. expanding the series about ordinary points
b. expanding the series about regular singular points where the indicial
equations have two unequal roots that differ by a non integral value
C. The student will demonstrate his/her ability to analyze various
kinds of "real-world” models from science and engineering by setting up and
solving
corresponding differential equations which are modeled after:
1. Newton’s Law of Cooling
2. growth and decay
3. vibration of a spring
4. simple electrical networks
5. orthogonal trajectories
XII. 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
withdraw 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.
XIII. 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 individual’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.
XIV. 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.
The ADA
Accommodations office is located in FSC 300 (205-856-7731).
