Spring 2004

MATH 365.00 (3 credits), M_W_F, 8:00AM-8:50AM, Wickersham 107

**Prerequisites:**A grade of C- or better in MATH 261 (

*Calculus III*) is the prerequisite for this course.**Instructor:**Dr. Buchanan

Office: Wickersham 218, Phone: 872-3659, FAX: 871-2320

Office Hours: 10:00AM-10:50AM (MTu_ThF), 9:00AM-9:50AM (W), or by appointment

Email:`Robert.Buchanan@millersville.edu`

URL:`http://banach.millersville.edu/~bob`**Textbook:***Elementary Differential Equations and Boundary Value Problems*, 7th edition, William E. Boyce and Richard C. DiPrima, John Wiley & Sons, Inc., New York, 2001, ISBN: 0-471-31999-6**Objectives:**MATH 365 provides an introduction to ordinary differential equations and their applications. Upon completion of this course the student will:

- be able to solve a variety of ordinary differential equations,
- appreciate the theory underlying the techniques of solution,
- be conversant with methods of applying ordinary differential equations in various applications.

**Course Contents:**- Topics covered in this course may include the following.
- First order ordinary differential equations (Chap. 2)
- Linear equations with variable coefficients (Sec. 2.1)
- Separable equations (Sec. 2.2)
- Modeling with first order equations (Sec. 2.3)
- Autonomous equations and population dynamics (Sec. 2.5)
- Exact equations and integrating factors (Sec. 2.6)
- Existence and uniqueness theory (Sec. 2.8)

- Linear differential equations of second order (Chap. 3)
- Homogeneous equations with constant coefficients (Sec. 3.1)
- Fundamental solutions of linear homogeneous equations (Sec. 3.2)
- Linear independence and the Wronskian (Sec. 3.3)
- Complex roots of the characteristic equation (Sec. 3.4)
- Repeated roots; reduction of order (Sec. 3.5)
- Non-homogeneous equations; method of undetermined coefficients (Sec. 3.6)
- Variation of parameters (Sec. 3.7)
- Mechanical and electrical vibrations (Sec. 3.8)
- Forced vibrations (Sec. 3.9)

- Series solutions of second order linear equations
(Chap. 5)
- Series solutions near an ordinary point (Sec. 5.2, 5.3)
- Regular singular points (Sec. 5.4)
- Euler equations (Sec. 5.5)
- Series solutions near a regular singular point (Sec. 5.6, 5.7)
- Bessel's equation (Sec. 5.8)

- The Laplace transform (Chap. 6)
- Definition of the Laplace transform (Sec. 6.1)
- Solution of initial value problems (Sec. 6.2)
- Step functions (Sec. 6.3)
- Differential equations with discontinuous forcing (Sec. 6.4)
- Impulse functions (Sec. 6.5)
- The convolution integral (Sec. 6.6)

- Systems of first order linear equations (Chap. 7)
- Review of matrices (Sec. 7.2)
- Systems of linear algebraic equations; linear independence, eigenvalues, eigenvectors (Sec. 7.3)
- Basic theory of systems of first order linear equations (Sec. 7.4)
- Homogeneous linear systems with constant coefficients (Sec. 7.5)
- Complex eigenvalues (Sec. 7.6)
- Fundamental matrices (Sec. 7.7)
- Repeated eigenvalues (Sec. 7.8)

If time permits other topics may be covered as well.

- First order ordinary differential equations (Chap. 2)
**Attendance:**Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (

*e.g.*homework assignments) prior to the absence. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final exam exemptions.**Homework:**Students are expected to do their homework and participate in class. Students should expect to spend a minimum of three hours outside of class on homework and review for every hour spent in class. Regularly homework problems will be assigned for collection and grading. Students should submit all homework by the date due. Late homework will not be accepted without valid excuse. Discussion between students on homework assignments is encouraged, but homework submitted for grading should be written up separately.

**Tests:**There will be three 50-minute in-class tests and a final examination. The tests are tentatively scheduled for

- Wednesday, February 11, 2004
- Friday, March 5, 2004
- Wednesday, April 14, 2004

**Grades:**Course grade will be calculated as follows.

Tests 55% Homework 20% Exam 25% I keep a record of students' test, homework, and exam scores. Students should also keep a record of graded assignments, tests, and other materials. The course letter grades will be calculated as follows. I will not ``curve'' course grades.

90-92 A 93-100 A 80-82 B 83-86 B 87-89 B 70-72 C 73-76 C 77-79 C 60-62 D 63-66 D 67-69 D 0-59 F **Inclement Weather Policy:**If we should miss a class day due to a school closing because of weather, any activities planned for that missed day will take place the next time the class meets. For example, if a test is scheduled for a day that class is canceled on account of snow, the test will be given the next time the class meets.

**Final Word:**Mathematics is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important. Organizing and conducting regular study sessions with other students in this class will help you to understand the material better.

Robert.Buchanan@millersville.edu

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