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