OAKTON COMMUNITY COLLEGE
CLASS SYLLABUS

MAT262, Ordinary Differential Equations, Fall 2004


 

Instructor
Prerequisite
Course Description
Learning Objectives
Academic Integrity
Outline of Topics
Methods of Instruction
Instructional Materials
Methods of Evaluation
Other Course Information
Homework Assignments


OAKTON COMMUNITY COLLEGE
CLASS SYLLABUS
 

Instructor: Tingxiu Wang, Ph.D. Semester: Fall 2004
Division Phone: 635-1688 Office Hours: MWF1:30--2:00pm or by appointment.
Office Phone: 635-1751 Office: Room 2142
e-mail:tingxiu@oakton.edu www.oakton.edu/~tingxiu/

I.Course
Prefix		Course
Number		 Course
Name		Credit:LectureLab
 MAT252 Ordinary Differential Equations330

II. Prerequisites:
MAT 252 or concurrent enrollment in MAT 252

III. Course (catalog) Description:
This course studies solutions of ordinary differential equations such as the first order differential equations, the linear equations of higher order, linear systems of differential equations, and their applications. The methods include separable equations, exact equations, homogeneous equations, direction fields, undetermined coefficients, variation of parameters, Euler-Cauchy equations, reduction of order, power series, and Laplace transforms. Calculators/computers will be used when appropriate.

IV. Learning Objectives:
  1. Solve first order differential equations by the methods such as separable equations, exact equations, homogeneous equations, linear equations, direction fields and numerical methods.
  2. Understand the existence and uniqueness of solutions, the structure of solutions of linear equations, and the concept of linear independence and its relationship to the Wronskian.
  3. Solve linear equations with constant coefficients by the methods of variation of parameters and undetermined coefficients.
  4. Solve linear systems of differential equations by the methods of elimination and eigenvalues.
  5. Use Laplace transforms in the solutions of equations.
  6. Use power series in the solution of equations.
  7. Applications of ordinary differential equations.

V. Academic Integrity:
The very nature of higher education requires that students adhere to accepted standards of academic integrity. Therefore, Oakton Community College has adopted a Code of Academic Conduct and a Statement of Student Academic Integrity. These may be found in the Student Handbook. You may also find a summary of the Code of Academic Conduct in the College Catalog. Among the violations of academic integrity listed and defined are: cheating, plagiarism, falsification and fabrication, abuse of academic materials, complicity in academic dishonesty, falsification of records and official documents, personal misrepresentation and proxy, and bribes, favors, and threats.
It is the student's responsibility to be aware of behaviors that constitute academic dishonesty.
Pursuant to the due process guarantees contained in the Policy and Procedures on Student Academic Integrity, the minimum punishment for the first offense for a student found in violation of the standards of academic integrity is failure in the assignment. In addition, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

VI. Outline of Topics:
  1. Introduction
    1. Ordinary differential equations
  2. First Order Differential Equations
    1. Linear equations
    2. Nonlinear equations
    3. Separable equations
    4. Exact equations
    5. Integrating factor
    6. Homogeneous equations
    7. Direction fields
    8. Existence and uniqueness
    9. Applications
  3. Higher Order Linear Equations
    1. Solutions of homogeneous equations
    2. Linear independence and the structure of solutions
    3. Reduction of order
    4. Homogeneous equations with constant coefficients
    5. Complex roots
    6. Nonhomogeneous equations
    7. The method of undetermined coefficients
    8. The method of variation of parameters
    9. Applications
  4. Numeric methods
    1. Direction fields
    2. Euler's method
    3. Modified Euler's method
    4. Runge-Kutta method
    5. Use of technology to demonstrate methods
  5. Series Solutions
    1. Review of power series
    2. Series solutions near ordinary points
    3. Series solutions near a regular singular point
  6. The Laplace Transforms
    1. Definition
    2. Solution of initial value problems
  7. Linear Systems of Differential Equations
    1. Linear systems and Matrices
    2. The method of elimination
    3. The method of eigenvalues
    4. Applications

VII. Methods of Instruction:
Methods of presentation can include lectures, discussion, and regularly assigned homework. Calculators/computers will be used when appropriate

VIII. Instructional Materials:
Differential Equations and Boundary Value Problems: Computing and Modeling, 3rd edition, by C.H. Edwards, Jr., and D. E. Penney. TI-89/92 is strongly recommended.

IX. Methods of Evaluation:
Evaluation methods can include grading homework, chapter or major tests, quizzes, and computer assignments.

Attendance: It is essential. You are responsible for all announcements and materials presented in the class.

Homework: There are daily assignments throughout the semester. This also includes some computer assignments.

Quizzes: There will be 9 take-home quizzes in this semester. The last quiz is cumulative. Attend every class to find out when a quiz is given. The due date of each quiz will be specified when it is given. No late quiz will be accepted. The lowest quiz will be dropped. Each quiz is worth 10 points.

Tests: There will be 3 exams. Each exam is worth 80 points. Every exam will be announced a week in advance. A make-up exam(except the last one) will be given only under a very special circumstance and if I am notified before the exam. To request a make-up, please give me a written note containing the information such as your name, class, and the date you like to take. The make-up exam may be more difficult than the classroom exam and must be made up within one week.

Extra Credit: The AMATYC Math Competition will be held on Wednesday, November 1, 2004, 1pm-3pm. You will receive an extra credit of 5 points for participation plus the points you get from the competition. The Math Competition Award Ceremony will be held on December 8, 2004. You will receive another extra credit of 8 points for participation. It is your responsibility to arrange the time to participate. There is no make-up. For more information about the competition, visit the web site at: http://servercc.oakton.edu/nsf-stem/

Grades: The maximum possible points available in this course are:

Quizzes - 80 points
Tests - 240 points

Total - 320 points

You course grade will be based on the percentage of the points you make to the total points available in the course:

A>=90%, B>=80%, C>=70% D>=60% F<60%.

X. Other Course Information:
  1. If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the ASSIST office in Instructional Support Services. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.
  2. Some deadlines:
    Saturday, September 18, 2004: Last day to withdraw and have course dropped from record.
    Last day to change to Audit. Saturday, October 16, 2004: Last day to withdraw with a “W”.
  3. It is suggested that you need to spend about 3 hours after each class to review the lecture note, read the textbook and do your homework.
    Homework Assignments
    SectionProblems
    1.15, 7, 9, 15, 21, 25, 27, 33, 35, 39, 41
    1.25, 7, 9, 15, 17, 23, 25, 27, 37
    1.31, 5, 9, odds 11-19
    1.4odds 1-28, 33-39
    1.53, 5, 11, 17, 25, 27, 33, 37
    1.6 part I: 3, 5, 11, 13, 17, 19, 23;
    part II: 25, 27, 29, odds 31-41, 59
    2.15, 7, 9, 11, 15, 19
    2.23, 5, 7, 9, 11
    2.3 1, 3, 5, 7, 9, 19
    2.4 1, 5, 9, 13
    2.5 1, 5, 9, 13
    2.6 1, 5, 9, 13
    3.1part I: odds 1-25, part II: odds 27-41
    3.2odds 1--25, 31
    3.3odds 5--41
    3.41, 3, 13, 15, 17(optional)
    3.54k+1, k=0, 1, 2, ……, 9, odds 45--55; optional 57, 59
    4.1 odds 1--29, 21(a)
    4.2 odds 1--29
    5.1 odds 1--19, 21--39
    5.2 odds 3--23, 27, 29
    7.1 1, 3, 9, odds 11--37
    7.2 odds 1-25, 29, 31, 33
    7.3 odds 1-23, 27, 31, 33
    7.4 odds 1--31, 37
    8.1 5, 7, 13, 15, 17, 21
    8.2 3, 5, 7, 17, 19, 21, 23, 29(optional)
    8.3 odds 1—31
WELCOME TO THIS CLASS