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MAT 204 Differential Equations Spring
2003 Instructor:
Bruce Armbrust, phone: 541-4660 ext. 314, email: armbrust@ltcc.edu Office Hours:
Room A210, Mon. & Wed. 9:30 - 10:30 AM
Fri. 10:00 – 11:00 AM GMC G4,
Tues. & Thurs. 11:00 AM - 12:00 PM And as always, by appointment. Class Time and Location:
Mon., Wed. 12:30 – 1:25 PM, E106
Tues., & Thurs. 12:30 - 1:40 PM, B107 Textbook: Elementary
Differential Equations, 7th
Edition, by Boyce, & DiPrima Course Description:
This course covers techniques of solving ordinary differential equations.
Topics include exact differential equations, separable equations, linear
equations, Bernoulli equations, integrating factors, the method of undetermined
coefficients, variation of parameters, series solutions, systems of differential
equations, and applications of differential equations. Prerequisite:
A grade of C or better in MAT 107. Course Objectives: The
successful student will: 1)
exhibit a proficiency in the topics covered in the
course; 2)
engage in logical and critical thinking; 3)
read technical information; and 4)
demonstrate the solution to problems by translating
written language into mathematical statements, interpreting information,
sketching relevant diagrams, analyzing given information, formulating
appropriate mathematical statements, and checking and verifying results. Course Grade:
Your final letter grade will be based on the usual grading scale: A 90-100%, B
80-89%, C 70-79%, D 60-69%, F 0-59% The
following items will make up the course grade: Homework:
150 points Exam1 (April
24) Exam2 (May
15):
500 points Exam3 (June
5) Final Exam
(June 25):
350 points Homework:
Homework will be due by 2PM the day after it is assigned.
Homework not turned in at this time will be considered late. You may turn
in homework up to one week after it is assigned for half credit.
If all homework is turned in, and no more than two are late, the lowest
regular exam score will be dropped. Exams:
Students are to bring a pencil and blank scratch paper to each exam.
If you cannot make it to an exam (final not included), you may take it up
to 2 school days prior to the scheduled date with proper arrangements.
Otherwise, the exam may be made up after the scheduled date with a
penalty of 10% per day. Registration Information: You
must register for this class at the Office of Admissions and Records.
You may drop the class with no penalty or mark on your record on or
before May 2. After April 26, you
may drop the class and receive a grade of W until June 6.
After June 6, if still enrolled, you will receive a grade of A, B, C, D,
F or I. How
to Succeed in a Math Class: I am often asked how to
successfully pass a math class, and here is my advice: I) Come to
every class session. Be prepared,
and plan on participating. II) Do your
homework. Remember that what I
assign is what I consider a bare minimum. If
you need more practice, do it. III) Read
the book. You paid good money for
it, so you might as well use it. IV) Make use
of available tutors and my office hours. You
will find tutors who know the subject matter in this course at the GMC. V) Do math
every day. Math is just like
everything else: if you don’t practice, you become rusty. Learning
Disabled Students: It is important that students
who are identified as being learning disabled speak to me about their special
needs. I am more than willing to
grant you reasonable accommodations. Academic
Dishonesty:
Academic dishonesty of any form will not be tolerated.
Students caught cheating on exams or quizzes will receive a score of zero
on the assignment for the first offense and a course grade of F for the second
offense. Students may work together
on homework assignments (and, in fact, are encouraged to) as long as all
students understand the material covered. Course Schedule: The
following is a tentative schedule. If
things change (and I have money that says they will), I will let you know. April
7
1.1/1.2
Introduction to Differential Equations 8
1.3/1.4
More Intro 9
2.1
Linear Equations with Variable Coefficients 10
2.2
Separable Equations 14
2.3
Modeling with First Order Equations 15
2.4
Linear vs. Nonlinear 16
2.5
Autonomous Equations 17
2.6
Exact Equations and Integrating Factors 21
2.8
The Existence and Uniqueness Theorem 22 2.9 First Order Difference Equations 23
3.1
Homogeneous Equations with Constant Coefficients 24
Exam I
April 28
Go Over Exam I 29
3.2
Linear Homogeneous Equations 30
3.3
Linear Independence and the Wronskian May 1
3.4
Complex Roots of the Characteristic Equation 5
3.5
Repeated Roots 6
3.6
Nonhomogeneous Equations
7
3.7
Variation of Parameters 8
3.8
Mechanical and Electrical Vibrations 12
3.9
Forced Vibrations 13
4.1
General Theory of nth Order Linear Equations 14
4.2
Higher Order Homogeneous Equations 15
Exam II
19
Go Over Exam II 20
4.3
Method of Undetermined Coefficients 21
4.4
Method of Variation of Parameters 22
5.1
Power Series 26
NO CLASS
MEMORIAL DAY 27
5.2
Series Solutions near an Ordinary Point 28
5.3
More Series Solutions 29
5.4
Regular Singular Points June
2
5.5
Euler Equations 3
6.1
The Laplace Transform 4
6.2
Initial Value Problems 5
Exam III 9
Go Over Exam III 10
6.3
Step Functions 11
6.4
Discontinuous Forcing Functions 12
7.2/7.3
Matrices/Systems of Linear Algebraic Equations 16
7.4
Systems of First Order Linear Equations 17
7.5
Homogeneous Linear Systems 18
7.6
Complex Eigenvalues 19
Review 25
Final Exam
Note: The final is from 12:00 - 1:50 PM |