COURSE
TITLE: Mathematics
289 B Differential Equations CREDIT HOURS: 4 credit hours
CONTACT
HOURS (including final exam): 62 hours
PREREQUISITE: A grade of C or better in Math 280, or a
grade of C or COREQUISITES:
None
better in Math 183 and concurrent enrollment in Math 280.
INSTRUCTOR: Thomas Kelley
CONTACT
INFORMATION: Office:
A-223 (Instructional
Telephone: (313) 845-6492 E-Mail: tkelley@hfcc.edu
Office
Hours: MWR 11:15 AM - 1 PM & 2:45 – 3:30 PM, Tues 11AM – Noon and
Fri 10 – 11:30 AM. Learning
Lab: Tuesday 12:08 – 1 PM
CATALOG
DESCRIPTION: This
course provides an introduction to ordinary differential equations by means of
numerical, graphical and algebraic analysis.
Topics covered include first order differential equations, second and
higher order linear equations, methods for nonhomogeneous
second order equations, series solutions, systems of first order equations and
COURSE
GRADING SCALE: A
through E Scale
COURSE
GOALS:
1.
To provide an introduction to the
nature and significance of differential equations for students of engineering,
mathematics, and science.
2.
To demonstrate various applications of differential equations to
problems from the physical sciences and engineering.
3.
To provide methods for solving differential equations which have proved
useful in a wide variety of applications.
4.
To present an exposition of differential equations which
incorporates graphical, numerical and algebraic analysis, without undue
emphasis on theoretical abstraction or routine mechanical manipulation.
5.
To use technology to graph solutions of ODE=s and to do explorations and
projects involving ODE=s.
6.
MAJOR CORE COURSE OBJECTIVES:
Upon successful completion
of this course students should be able to:
1.
Recognize common forms of differential equations such as first order
separable, exact, and homogeneous, first order linear, linear with constant
coefficients and know which methods to apply.
Utilize these methods to obtain solutions subject to possible initial or
boundary value conditions.*
2.
Use technology in order to develop calculus-based graphical methods as
well as numerical methods to verify explicit solutions and to obtain partial or
approximate solutions to problems that cannot be solved by explicit methods. Recognize the limitations of such methods*.
3.
Solve and analyze simple systems of differential equations and use
4.
Use variation of parameters and series to solve linear differential
equations with non-constant coefficients. Use series methods and successive
approximations to obtain numerical results.
5.
Apply these techniques to problems in the physical sciences. This will
consist of developing models of phenomena in terms of differential equations,
solving these equations utilizing numerical, graphical and/or algebraic
methods, and interpreting the results in light of the original problem*.
* = fulfills HFCC General
Education Outcome for critical thinking and problem solving
ASSESSMENT OF ACADEMIC
ACHIEVEMENT:
All students will be
required to complete a comprehensive final examination that assesses the
learning of all course objectives. This exam must be weighted in a manner so
that this exam score is worth a minimum of fifteen percent of the final course
grade. In selected semesters this exam may be a common exam administered to all
sections of Math 289. All additional
assessment of student achievement is left to instructor discretion. Some exam
problems should require the use of a graphing calculator.
GENERAL
COURSE REQUIREMENTS AND RECOMMENDATIONS:
All Sections: A
graphing calculator is required of each student. The Mathematics Division recommends and uses
the TI-83 or TI-83 Plus Graphing Calculator.
TEXTBOOK: Fundamentals of Differential Equations: by Nagle, Saff, and Snider
- 7th ed.
(Pearson Education,Inc.; ISBN:
0-321-38841-0)
Optional: Student=s Solution Manual by Maymeskul (Pearson; ISBN: 0-321-38845-3)
CORE
COURSE TOPICS:
Chapter 1 Introduction (Sec
1.1-1.4)
Chapter 2 First
Order Differential Equations (Sec
2.1-2.4, 2.6)
Chapter 3 Mathematical
Models and Numerical Methods
Involving First-Order Equations (Sec 3.1-3.4, 3.5
- 3.7)
(3.5 - 3.7 are optional)
Chapter 4 Linear
Second-Order Equations (Sec
4.1-4.7, 4.9, 4.10)
Chapter 5 Introduction
to Systems and Phase Plane Analysis (Sec
5.2)
(This may be postponed until doing 7.9)
Chapter 6 Theory
of Higher-Order Linear Differential Equations (Sec
6.1, 6.2)
Chapter 7 Laplace
Transforms (Sec
7.8 is optional) (Sec
7.1 - 7.9)
Chapter 8 Series
Solution of Differential Equations (Sec 8.6 is optional) (Sec 8.1 - 8.3, 8.6)
INSTRUCTIONAL
POLICIES:
Assignments: Routine homework problems will be assigned at each class to be
turned in at the next class. Worksheet
homework will be distributed and is usually due one week from the distribution
date. Homework will be graded and
returned. Suggested exercises will be given and the student is strongly
encouraged to do them. They are not handed in, but questions on them during
class or office hours are welcome.
Attendance: Attendance will be noted at each class session. If you miss a class you are responsible for
finding out what you missed and making arrangements for making up the
work. Office hours are for questions not
answered in class; they are not
make-up classes.
Grading
Procedures: At least three “in-class”
exams will be given during the semester with at least one week’s notice given
before the date of the exam. The grade
on homework will count as 1 “in-class” exam.
The Final exam will be given as scheduled by the college and counts from
25 – 33% of your course grade.
Grading
Policy: Grades are based on the scale: 90 – 100 = A range. 80 – 89 = B range.
67 – 79 = C range. 55 – 66 = D range. Less than 55 = E.
Missed Examination: If you must miss an exam for
a very good reason, let me know as
soon as possible. Arrangements may be
made to take an exam early, but do not expect to be able to make up an exam if
you let me know after the fact. It is
the student’s responsibility to contact me as soon as possible
concerning a missed exam.
Drop Policy:
College Policy: Students may
officially drop a class and receive a DR grade anytime up until the end of the
day Thursday, November 6, 2008. If a
student stops attending without officially withdrawing, the instructor may
record either an E or a DR grade.
Instructor Policy: Students may
receive a DR grade if they make a request for the grade in writing to the
instructor before noon on Friday, December 5, 2008.
Academic
Dishonesty:
College Board of Trustees
Policy #8500
(adopted 3/17/97):
A...It shall be the policy of
the College that determination of the fact of academic dishonesty by a student
shall be a matter of individual judgment by the instructor. The instructor may administer a penalty up
to, and including, failure in the particular course...@
Instructor Policy: Academic dishonesty of any form will be
grounds for immediate failure in the course and the recording of a final grade
of E in the course. To insure the
integrity of test scores, students are not allowed to leave the classroom
during tests.
MATHEMATICS
DIVISION POLICY ON CUT-OFF DATE FOR STUDENT DROP-DOWNS
A registered students may only drop-down (move-up) to another math class
within the first three weeks of the
Fall and Winter semesters. In the Spring and/or Summer semesters, students have only one and one-half weeks to drop-down
(move-up) to another class. In order to
drop-down (move-up), a student must:
Obtain the written
permission of his/her current instructor stating that the student was
misplaced,
See the Mathematics
Division Director for assistance in finding open sections, and
Obtain the written
permission of the instructor in the new lower (higher) course.
The student must then officially
file an Add-Drop form at the Registration office.