Description:

This course will cover standard types of equations that involve rates of change. In particular, this is an introductory course in equations that involve ordinary derivatives. Both qualitative and quantitative approaches will be used. Standard types and methods will be covered, including Laplace transforms and numerical methods. 3 hrs./wk. Beginning summer 2009 this course will be replaced by the 4-credit-hour course MATH 254 Differential Equations.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor's course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Calculate solutions to higher-order ordinary differential equations.
2. Calculate solutions to first-order ordinary differential equations.
3. Calculate solutions to systems of first-order ordinary differential equations.
4. Utilize the concepts of differential-equation theory in applied modeling activities.

Content Outline & Competencies:

I. Introduction
   A. Define ordinary versus partial differential equations.
   B. Define the degree of a differential equation.
   C. Define linear versus nonlinear differential equations.
   D. Define a solution to a differential equation.
   E. Utilize direction fields in solving differential equations.

II. First-Order Differential Equations
   A. Introduce the existence and uniqueness theorem.
   B. Calculate solutions to linear first-order ordinary differential
equations.
   C. Calculate solutions to separable first-order ordinary differential
equations.
   D. Utilize first-order ordinary differential equations in modeling
activities.

III. Numerical Methods
   A. Define the Euler method.
   B. Define improvements on the Euler method.
   C. Introduce the Runge-Kutta methods.
   D. Utilize numerical methods in solving first-order initial-value
problems.
	
IV. Systems of Differential Equations
   A. Define higher-order linear differential equations
   B. Transform higher-order linear differential equations to systems of
first-order differential equations.
   C. Review matrices and aspects of linear algebra.
   D. Utilize the eigenvalue-eigenvector method in solving systems of
homogeneous linear differential equations with constant coefficients.
   E. Define linear dependence and independence.
   F. Utilize the Wronskian to determine the linear independence of
solutions of equations.
   G. Calculate solutions given real distinct, real repeated, and complex
roots of the characteristic equation.
   H. Define fundamental solutions of linear homogeneous equations.
   I. Construct the general solution of nonhomogeneous linear systems
utilizing the method of variation of parameters.
   J. Introduce stability considerations.
   K. Utilize the phase plane in solving systems.
   L. Analyze the solutions of almost linear systems.
   M. Utilize systems of differential equations in modeling activities.

V. The Laplace Transform
   A. Define the Laplace transform.
   B. Utilize Laplace transforms in solving initial-value problems.
   C. Introduce step functions.
   D. Introduce discontinuous forcing functions.
   E. Introduce impulse functions.
   F. Utilize the Convolution theorem

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers and/or Unit Projects  40% - 80%
Homework, Quizzes and/or Small Projects        0% - 50%
Final Exam**                                  10% - 40%

**The final exam must count at least as much as any unit exam, unit paper
or unit project. In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course. At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level math course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.