Instructor:         Tingxiu Wang, Ph.D.                                                     Semester:   Spring, 2000
Division Phone: 635-1688                                                                     Office Hrs: MWF 11:00am-12:00pm
                                                                                                                              or by Appointment
Office Phone: 635-1751                                                                        Office:   Room 2142 (at DP)

I. Course            Course              Course
   Prefix              Number             Name                  Credit:                Lecture                   Lab

   MAT                 262       Ordinary Differential          3                        3                           0
                                                Equations

II. Prerequisites for the Course:

    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. Course Objectives:
 
 1. Solve first order differential equations by the methods such as separable equations, exact equations, homogeneous equations, linear equations, and direction fields.
 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.

V. Complete Course Outline :

 1. Introduction
  A.  Ordinary differential equations

 2. First Order Differential Equations
  A. Linear equations
  B. Nonlinear equations
  C. Separable equations
  D. Exact equations
  E. Integrating factor
  F. Homogeneous equations
  G. Direction fields
  H. Existence and uniqueness
  I.  Applications

 3. Higher Order Linear Equations
  A. Solutions of homogeneous equations
  B. Linear independence and the structure of solutions
  C. Reduction of order
  D. Homogeneous equations with constant coefficients
  E. Complex roots
  F. Nonhomogeneous equations
  G. The method of undetermined coefficients
  H. The method of variation of parameters
  I. Applications

 4. Series Solutions
  A. Review of power series
  B. Series solutions near ordinary points
  C. Series solutions near a regular singular point
 
 5. The Laplace Transforms
  A. Definition
  B. Solution of initial value problems

 6. Linear Systems of Differential Equations
  A.  Linear systems and Matrices
  B. The method of elimination
  C. The method of eigenvalues
  D. Applications

VII.  Methods of Instruction:

 Methods of presentation include lectures, discussions, and regularly assigned homework.  Calculators/computers will be used when appropriate.
 VIII. Instructional Materials:

 Differential Equations and Boundary Value Problems:Computing and Modeling, 2nd edition,
 by C.H. Edwards, Jr., and D. E. Penney.

IX. Methods of Evaluating Student Progress:

 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.  A late work turned before the next class meeting will carry a two-point penalty.  No late quiz will be accepted after that.  The lowest quiz will be dropped. Each quiz is worth 10 points.
 
 Tests:  There will be 4 exams.  Each exam is worth 60 points.  Every exam will be announced a week in advance.  A make-up exam(except the final) 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.

 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:

a. 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.
 b. Some deadlines:

 Saturday, February 12, 2000: Last day to withdraw and have course dropped from record.
     Last day to change to Audit.
 Saturday, March 11, 2000: Last day to withdraw with a “W”.

c. It is suggested that you need to spend about 2 hours after each class to review the lecture note, read the textbook and do your homework.

Homework Assignments:

Section  Problems
1.1  5, 7, 9, 15, 21, 25, 27, 33, 35, 39, 41
1.2  5, 7, 9, 15, 17, 19, 21, 23, 33
1.3  1, 5, 9, 15, 17, odds 21-29, 31
1.4  odds 1--35, 43
1.5  3, 5, 11, 17, 19, 25, 27, 33, 37
1.6  part I: 3, 5, 11, 13, 17, 19, 23;
  part II:  25, 27, 29, odds 31-41, 47

2.1  1, 3, 5, 7, 11, 15
2.2  3, 5, 7, 9, 11
2.3  1, 3, 5, 7, 9, 19

3.1  part I: odds 1-25, part II: odds 27-41
3.2  odds 1--25, 31
3.3  odds 5--41
3.4  1, 3, 13, 15, 17 (optional)
3.5  4k+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, (optional)29
8.3  odds 1--31