Northeastern State University
College of Mathematics, Science and
Nursing
Department of Mathematics
Tahlequah, OK
INSTRUCTOR:
Dr. John C.D.
Diamantopoulos, Office: SC 251
Office Hours:
10:30-11:30am & 2-3pm MW, 2-3pm F, and 10-11am TTh
(Tahlequah Campus)
5-5:30pm and 8:35-9:05 TTh (Broken Arrow Campus)
Telephone: 918-444-3807
FAX: 918-458-2325
E-mail: diamantj@nsuok.edu Web Page: http://arapaho.nsuok.edu/~diamantj
COURSE
TITLE AND NUMBER: CLASS
DAYS & TIME:
MATH 4113 - Differential Equations 5:30-6:45pm TTh
Fall 2008
PREREQUISITES:
Math 2624,
Calculus II
CATALOG
DESCRIPTION OF COURSE:
Introduction to
the theory and application of ordinary differential equations, linear and non-linear
first order equations, second order linear equations and higher order linear
equations. Introduction to the Laplace transform and applications.
COURSE
PURPOSE:
This course
provides students an opportunity to develop their calculus skills in a more
sophisticated setting than the first year calculus sequence. Students use differential equations to model
physical phenomena, business applications, and applications in medicine and
biology. The course is particularly
useful to a student studying a physical science or mathematics. The student will see connections to a broad
range of mathematics including complex functions, linear algebra, advanced
calculus, topology, numerical analysis, special functions, and discrete
mathematics.
EXPECTED
COURSE OUTCOMES:
The
student will be expected to achieve the following objectives:
1. Distinguish different types of
differential equations.
2. Solve
linear, separable, homogeneous, Bernoulli, and exact first order equations.
3. Find the
interval on which a solution to a given differential equation exists.
4. Model and
solve real-world problems using linear or separable differential equations.
5. Analyze the
behavior of solutions of differential equations as the independent variable
approaches a limiting value.
6. Convert
certain types of second order equations to first order equations by an
appropriate substitution.
7. Identify and
solve second and higher order linear equations with constant coefficients, both
homogeneous and non-homogeneous.
INSTRUCTIONAL
MATERIALS:
Fundamentals of Differential Equations, 7th Edition, by Nagle, Saff
and Snider, 2008 (Addison Wesley Longman).
INSTRUCTIONAL
PROCEDURES:
The expected
course outcomes will be realized through a variety of instructional strategies
to aid the students’ construction of cognitive schemas. Those strategies include, but are not limited
to, the following: expository-discussion, demonstration, inquiry, and group
activities. The instructor also will assign homework exercises to ensure that
students are learning the material as the semester progresses.
Differential Equations – Course Outline
1.
Chapter 1 - Introduction
1.1
Background
1.2 Solutions and
Initial Value Problems
1.3 Direction
Fields
1.4 The
Approximation Method of Euler
2. Chapter
2 - First Order Differential Equations
2.1 READ:
“Introduction: Motion of a Falling Body”
2.2 Separable
Equations
2.4 Exact
Equations
2.3 Linear
Equations
2.5 READ: “Special Integrating Factors”
2.6 Substitutions and Transformations
** Major Examination #1 (Sections:
1.1-1.4, 2.2-2.6)
3. Chapter
3 - Mathematical Models and Numerical Methods
3.1 READ:
“Mathematical
Modeling”
3.2 Compartmental
Analysis (Mixing and Population problems)
3.3 Heating and
Cooling of Buildings
4. Chapter
4 - Linear Second Order Equations
4.1 READ:
“Introduction: The
Mass-Spring Oscillator”
4.2 Homogeneous
Linear Equations: The General Solution
4.3 Auxiliary
Equations with Complex Roots
** Major Examination #2
(Sections: 3.2-3.3, 4.2-4.3)
Chapter 4 - Linear Second Order
Equations (Cont.)
4.4 Non-Homogeneous
Equations: The Method of Undetermined Coefficients
4.5 The
Superposition Principle and Undetermined Coefficients Revisited
4.6 Variation of
Parameters
** Major Examination #3
(Sections: 4.4-4.6)
Chapter 7 - Laplace Transforms
7.1
READ:
“Introduction: A Mixing Problem”
7.2
Definition of the Laplace Transform
7.3
Properties of the Laplace Transform
** Final Examination: Comprehensive
STUDENT
PERFORMANCE ACTIVITIES:
(Attendance/Punctuality)
Regular class
attendance is required. Plan to get
notes and handouts from other students if you are unable to attend a
class. Students are not permitted to
leave and return to class during a class period. Students are not permitted to bring food or
drink to class. No visitors without
instructor’s prior consent. The student
may seek assistance from the Mathematics Department tutor in the Science
Building, SC 264.
ASSIGNMENT
DUE DATES:
Homework
assignments are due at or before the beginning of the class period on
the date indicated when the assignment is given; please just place on the front
desk as you get to class.
Homework will be
turned in as a group assignment, preferably a group of two people (but I would
permit a group of three if necessary). Reading
assignments (which will consist of the next section or portion of material to
be covered in the text) are considered preparation for the lecture period and
should be done prior to class time.
The student is responsible for all material assigned even if not
discussed in class. Homework should be written-up in a neat and organized
fashion. (if multiple pages are needed, please staple them
together) Homework which does not
meet the above guidelines will be given a zero!
** While
discussion among classmates/groups on homework problems is expected (and even
encouraged), direct copying from one paper to another will not be
tolerated!
STUDENT
EVALUATION:
Grades will be
based upon formal written examinations, HW/quizzes, and a final examination:
3 Examinations during
term....................... 300 points
Homework………..................................... 200
points
Final Examination...................................... 100
points
1. Several
homework grades of 50 points each will be given throughout the semester. The lowest one will be dropped in determining the HW grade. No make-ups on missed HW. The HW scores will be totaled and normalized
to reflect a possible 200 points.
2.
No
make-ups allowed on exams unless due to an excused absence and the instructor
is notified prior to the exam.
Students who miss an exam (or exams) may count their score on the
comprehensive final for one missed exam.
Students who arranged their other activities around test schedules and
complete each exam when administered will be allowed to replace their lowest
exam score with their score on the comprehensive final. You can not replace
the final exam score with one of the hour exams and the final exam must be
taken and counted in your final grade total!
3.
All
hour exams will be in-class exams in
which you will be allowed to use a one
page summary sheet containing definitions, formulas, and outlines of
methods/processes for reference but nothing
additional (e.g., regular notes, worked out examples, etc.). Be advised to study and prepare for them as
if they were closed note exams and
use your summary sheet only as a reminder of ideas/techniques studied!
4. Performance
on examinations and subsequent cumulative course averages will be based upon
standard definitive grade values as indicated below:
90 - 100 = A 60 - 69 = D
80 - 89 = B Below
60 = F
70 - 79 = C
5. The
final examination will be administered on Thursday, December 18 at
5:30-7:25pm
A.
August
27 Last day to add a
class or enroll
B.
September
1 Labor Day!!!
C.
September
3 Last day to drop (refund)
D.
October
16-17 Fall
Break!!!
E.
November
12 Last day to drop with an
automatic “W”
F.
November
26-30 Thanksgiving Break!!!
G.
December
12 Last day to drop a single
class (“W” is not automatic) or withdraw from the university
H.
December
18 Final Exam, 5:30-7:25pm
7. Academic
integrity is expected of everyone in this class. Any instance where cheating occurs on HW will
first be given a warning, and subsequent occurrences will result in a zero on
that assignment. Any instance of
cheating on an exam will result in a zero on the exam without the possibility
of it being replaced by the final exam score.
8. Any
needed additions/deletions to this syllabus will be clearly stated during class
time(s).
ADA
COMPLIANCE:
If any member of
the class feels that he/she has a disability and needs special accommodations
of any nature whatsoever, the instructor will work with you and the
University's Office of Student Affairs to provide reasonable accommodations to
ensure that you have a fair opportunity to perform in this class. Please advise the instructor of such
disability and the desired accommodations at the first class attended.
INCLEMENT
WEATHER / DISASTER POLICY:
The following
are basic premises for the inclement weather policy at Northeastern State
University:
1. Classes
are expected to be held if at all possible.
2. It
is the student's responsibility to receive the information when weather is
questionable.
3. Neither
students nor faculty are expected to risk life or limb.
4. Faculty
members are obligated to hold classes if the University is not closed, unless
the faculty member is unable to get to campus.
Policy: During times of inclement weather, decisions concerning day
classes will be made by 6:00 a.m. in order for the media to be notified and for
students to receive the announcement before they leave home. Decisions
concerning night classes will be made by 3:00 p.m.
The
following media will be notified regarding closing of the campus:
Radio Stations: Television
Stations:
KRMG 740 AM Tulsa KJRH
Channel 2 Tulsa
KAYI 107 FM Tulsa KOTV Channel 6 Tulsa
KTLQ 1350 AM Tahlequah KTUL
Channel 8 Tulsa
KEOK 102 FM Tahlequah KFSM
Channel 5 Fort Smith
KBIX 1490 AM Muskogee Cable
Channel 99 Tahlequah
KMMY 97 FM Muskogee
KVOO 1170 AM Tulsa
The
automated attendant message on 918-456-5511 will be modified to include
information concerning campus operations during inclement weather.