Ordinary Differential Equations
MATH 365.02 (3 credits), Tu_Th, 1:00PM-2:15PM, Wickersham 107
A grade of C- or better in
MATH 261 (Calculus III)
is the prerequisite for this course.
Office: Wickersham 112, Phone: 872-3659, FAX: 871-2320
Office Hours: 10:00AM-10:50AM (MTu_ThF), or by appointment
Elementary Differential Equations and Boundary Value Problems,
William E. Boyce and Richard C. DiPrima,
John Wiley & Sons, Inc.,
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)
- Nonhomogeneous 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
- 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.
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.
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.
There will be three 50-minute in-class tests and a final examination.
The tests are tentatively scheduled for
The final examination
(Thursday, May 9, 2002 10:15AM-12:15PM) will be comprehensive.
I will not ``curve'' test or exam grades.
- Thursday, February 21, 2002
- Thursday, March 28, 2002
- Tuesday, April 30, 2002
Course grade will be calculated as follows.
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.
- Final Word:
Math 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.
Page maintained by: Robert.Buchanan