Syllabus
DIFFERENTIAL EQUATIONS / MA523
SPRING SEMESTER 2007
INSTRUCTOR:
Office: Room
#101(Class in 208) Phone: 357-3174 ext. 129 e-mail: MJamil@lsmsa.edu
TEXT: 1) Elementary
Differential Equations; 7th edition by Earl D. Rainville
& Phillips E. Bedient
2)
The Ultimate ODE Power Tool (ODE Architect Compaion)
CODEE by John Wiley & Sons Inc.
COURSE This
course is a study of ordinary differential equations, including linear
equations, systems
DESCRIPTION: of
equations, equations with uniqueness of solutions, methods, boundary value
problems, and
applications.
COURSE In
order to demonstrate that a student is in the process of achieving the major
course objectives, the
REQUIREMENT: student
must be able to work problems on major tests and quizzes similar to those
problems
regularly assigned as homework. 5% of the grades are taken from homework
assignments,
homework
is an integral part of the course and provides the means by which the student
can learn
mathematical
concepts. It is doubtful that the
student will be able to pass the course without working
the
homework assignments.
ATTENDANCE: Students
are expected to be present and on time to every class. Attendance, including tardiness, will
be recorded and turned in daily. Students should note that absence from class,
excused or
unexcused,
does not automatically give students the right to postpone quizzes or tests
that follow.
Unexcused absences
and Tardiness will negatively affect the final grade.
RULES FOR 1. If any student has legitimate reason for
being unable to take a test on any of the
TEST TAKING: scheduled test dates, that student must notify Mr. Jamil at least 2 days
before the exam unless
excused by the school.
2.If a student fails to take an exam or quiz on the
scheduled test date without previously notifying Mr.
Jamil, 10% points will be taken off of that
student's test grade, and NO
bonus points will be available for that student.
GRADING There
will be five tests and a final. Pop
quizzes and assignments will be administered throughout the
PROCEDURE: the course.
One test and a quiz will be dropped before the final grade is given. Any
test may be
cumulative. The
final exam will be comprehensive. The
break-up is as follows:
Tests 60%
Pop quizzes 10%
Assignments & class participation 10%
Final 20%
OFFICE
HOURS: M 10:00 – 11:00,
T 9:30 – 11:30, 2:00 – 2:30 & 3:30 –
4:30
W 10:00
– 11:00 R 10:30 – 12:00
F 10:00
– 11:00 By
appointment only: T 1:30,
W 8:00 & R 2:00
GUIDED
STUDY: Mondays 4:00
– 5:30 pm
DIFFERENTIAL
EQUATIONS (MA523) / SPRING SEMESTER 2005
WEEK DATE TOPIC IN
TEXT
1 1 – 8 – 2007 Introduction, Definitions, and review of integrals 1-2/pg. 1-3
The
elimination of arbitrary constant 3/pg.
6
Families
of curves & The isoclines of an equation 4-5/pg. 17
2 1
– 15 (Read the
Existence Theorem), Separation of variables 7/pg.
21
Homogeneous
functions 8/pg.
26
3 1
– 22 Equations
with homogeneous coefficients 9/pg.
28
1 – 24 – 2007 TEST
# 1
4 1
– 29 Exact equations 10/pg
32
The
linear equation of order one 11/37
The
general solution of a linear equation, Applications 12/pg. 41, 47
5 2
– 5 Integrating
factor found by inspection 18/pg.
63
The
determination of integrating factor 19/pg.
67
6 2 – 12 Substitution suggested by the equation 20/pg. 67
2 – 15 – 2007 TEST # 2
7 2 – 19 – 2007 Mardi Gras Holidays
8 2
- 26 Bernoulli's equation 21/pg.
74
Coefficients
linear in the two variables 22/pg.
77
9 3 – 5 The general linear equation & An existence and
uniqueness Theorem 24-25/pg.
87-89
10 3
– 12 Linear
independence & The Wronskian 26-27/pg. 90-91
General
solution of homogeneous equation 28/pg.
94
3 – 15 – 2005 TEST # 3
11 3 – 19 General
solution of nonhomogeneous equation 29/pg. 96
Differential
Operators & The fundamental laws of operation 31/pg. 100
Some
properties of differential operators 32/pg.
102
12 3 – 26 The auxiliary equation; distinct roots 34/pg. 105
The auxiliary roots; repeated roots 35/pg.
108
A definition of exp z for imaginary z 36/pg. 112
13 4
– 2 The auxiliary equation; imaginary roots & Hyperbolic
funs. 37-38/pg. 114-116
Construction
of a homogeneous equation from a 39/pg.
121
specified solution
4 – 5 – 2007 TEST # 4
14 4
– 9 – 2007 Spring Break
15 4 – 16 Solution
of a non homogeneous equation 40/pg.
124
The
method of undetermined coefficients 41/pg.
126
Solution
by inspection 42/pg.
132
Introduction
& Reduction of order 43-44/pg.139
16 4 – 23 Variation of parameters 45
/ pg. 143
Solution
of y''
+ y = f(x) 46
/ pg. 148
The
exponential shift 47
/ pg. 152
4 – 26 – 2007 TEST #
5
The
inverse differential operator, 1 / f(D) 48 / pg. 156
Evaluation
of [ 1 / f(D) ] eax 49
/ pg. 157
Evaluation of
(D2+ a2 ) -1sinax &
(D2+ a2 ) -1cosax 50 / pg. 158
17 4
– 30 Inverse
Laplace transformation 70
/ pg. 209
Catch
Up – Numerical solution will be added if the time permit
18 5 – 7 – 2007 Finals
The Instructor reserves the right to change any
portion of this class guide by announcing the change during a scheduled class
meeting.
J