Ordinary Differential Equations

I.     Course Prefix/Number: MAT 262

       Course Name: Ordinary Differential Equations

       Credits: 3 (3 lecture; 0 lab)

II.    Prerequisite

MAT 252 with a minimum grade of C.

III.   Course (Catalog) Description

Course presents the solution of ordinary differential equations with applications, power series, Laplace transformations, systems of linear differential equations and numerical methods. Technology will be used when appropriate.

IV.   Learning Objectives

  1. Solve first order differential equations by methods such as separable equations, exact equations, homogeneous equations, linear equations, and direction fields.
  2. Solve linear differential equations by demonstrating the existence, uniqueness, and structure of solutions, including linear independence and its relationship to the Wronskian.
  3. Solve linear differential 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. Solve differential equations using Laplace transforms.
  6. Solve differential equations using power series.
  7. Solve differential equations using numerical methods, and classify the limitations of those methods.
  8. Model and solve physical problems using methods presented in the course, including use of appropriate calculator and computer technology.

V.    Academic Integrity and Student Conduct

Students and employees at Oakton Community College are required to demonstrate academic integrity and follow Oakton's Code of Academic Conduct. This code prohibits:

• cheating,
• plagiarism (turning in work not written by you, or lacking proper citation),
• falsification and fabrication (lying or distorting the truth),
• helping others to cheat,
• unauthorized changes on official documents,
• pretending to be someone else or having someone else pretend to be you,
• making or accepting bribes, special favors, or threats, and
• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, 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.

Please review the Code of Academic Conduct and the Code of Student Conduct, both located online at

VI.   Sequence of Topics

  1. First Order Differential Equations
    1. Linear equations
    2. Separable equations
    3. Exact equations
    4. Integrating factors
    5. Use of technology to solve differential equations and systems
  2. Higher Order Linear Differential Equations
    1. Existence, uniqueness and structure of solutions
    2. Homogeneous equations
    3. Reduction methods for order of equations
    4. Homogeneous equations with constant coefficients
    5. Complex roots of auxiliary equations
    6. Nonhomogeneous equations
    7. Method of undetermined coefficients
    8. Method of variation of parameters
    9. Use of technology to support calculations
  3. Applications and modeling
    1. Growth and decay
    2. Mechanics
    3. Vibrations
    4. Spring-mass systems
    5. Electric circuits
    6. Numerical techniques
  4. Systems of differential equations
    1. Elimination method
    2. Eigenvalue method
    3. Use of technology to demonstrate methods
  5. Laplace transform
    1. Properties of the Laplace transform
    2. Inverse transform and solution of initial value problems
    3. The Laplace transform of discontinuous functions
    4. Convolutions calculated by the Laplace transform (optional)
    5. Dirac Delta function (optional)
    6. Use of technology to calculate Laplace transforms
  6. Power series
    1. Power and Taylor series
    2. Regular and ordinary singular points

VII.  Methods of Instruction

(To be completed by instructor)

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate.  Mathematica, Derive, and TI-92 Calculators are available for use at the College at no charge.
Course may be taught as face-to-face, hybrid or online course.

VIII. Course Practices Required

(To be completed by instructor)

Course may be taught as face-to-face, hybrid or online course.

IX.   Instructional Materials

Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words “View Book Information”.

Textbooks can also be found at our Mathematics Textbooks page: http://www.oakton.edu/academics/academic_departments/math/syllabi

A computer algebra system is required.  Mathematica, Derive or use of a TI-89 or a TI-92 is recommended.

X.    Methods of Evaluating Student Progress

(To be determined and announced by the instructor)

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

The following applies to the online section of this course only.

This online course requires that students take their exams as directed by their instructor: either on campus at Oakton's Testing Center, at an authorized testing center with a face-to-face monitor, or remotely through a pre-approved testing service.   (To be customized by instructor.)

XI.   Other Course Information

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

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 Access and Disability Resource Center at the Des Plaines or Skokie campus. 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.

Oakton Community College is committed to maintaining a campus environment emphasizing the dignity and worth of all members of the community, and complies with all federal and state Title IX requirements.

Resources and support for
  • pregnancy-related and parenting accommodations; and
  • victims of sexual misconduct
can be found at www.oakton.edu/title9/.

Resources and support for LGBTQ+ students can be found at www.oakton.edu/lgbtq.

Electronic video and/or audio recording is not permitted during class unless the student obtains written permission from the instructor. In cases where recordings are allowed, such content is restricted to personal use only. Any distribution of such recordings is strictly prohibited. Personal use is defined as use by an individual student for the purpose of studying or completing course assignments.

For students who have been approved for audio and/or video recording of lectures and other classroom activities as a reasonable accommodation by Oakton’s Access Disabilities Resource Center (ADRC), applicable federal law requires instructors to permit those recordings. Such recordings are also limited to personal use. Any distribution of such recordings is strictly prohibited.

Violation of this policy will result in disciplinary action through the Code of Student Conduct.