##### 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 minimum grade of C.

**III. Course (Catalog) Description **

Course presents the solution of ordinary differential equations. Content includes applications, power series, Laplace transformations systems of linear differential equations, and numerical methods. Calculators/computers 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. 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 and numerical models.

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 and numerical models.

**V. Academic Integrity **

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.

Details of the Code of Academic Conduct can be found in the Student Handbook.

• 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.

Details of the Code of Academic Conduct can be found in the Student Handbook.

**VI. Sequence of Topics **

1. First Order Differential Equations

a. Linear equations

b. Separable equations

c. Exact equations

d. Integrating factors

e. Use of technology to solve differential equations and systems

2. Higher Order Linear Differential Equations

a. Homogeneous equations

b. Reduction methods for order of equations

c. Homogeneous equations with constant coefficients

d. Complex roots of auxiliary equations

e. Nonhomogeneous equations

f. Method of undetermined coefficients

g. Method of variation of parameters

h. Use of technology to support calculations

3. Applications and modeling

a. Growth and decay

b. Mechanics

c. Vibrations

d. Spring-mass systems

e. Electric circuits

f. Numerical techniques

4. Systems of differential equations

a. Elimination method

b. Eigenvalue method

c. Use of technology to demonstrate methods

5. Laplace transform

a. Properties of the Laplace transform

b. Inverse transform and solution of initial value problems

c. The Laplace transform of discontinuous functions

d. Convolutions calculated by the Laplace transform

e. Use of technology to calculate Laplace transforms

6. Power series

a. Power and Taylor series

b. Regular and ordinary singular points

c. Frobenius' method

a. Linear equations

b. Separable equations

c. Exact equations

d. Integrating factors

e. Use of technology to solve differential equations and systems

2. Higher Order Linear Differential Equations

a. Homogeneous equations

b. Reduction methods for order of equations

c. Homogeneous equations with constant coefficients

d. Complex roots of auxiliary equations

e. Nonhomogeneous equations

f. Method of undetermined coefficients

g. Method of variation of parameters

h. Use of technology to support calculations

3. Applications and modeling

a. Growth and decay

b. Mechanics

c. Vibrations

d. Spring-mass systems

e. Electric circuits

f. Numerical techniques

4. Systems of differential equations

a. Elimination method

b. Eigenvalue method

c. Use of technology to demonstrate methods

5. Laplace transform

a. Properties of the Laplace transform

b. Inverse transform and solution of initial value problems

c. The Laplace transform of discontinuous functions

d. Convolutions calculated by the Laplace transform

e. Use of technology to calculate Laplace transforms

6. Power series

a. Power and Taylor series

b. Regular and ordinary singular points

c. Frobenius' method

**VII. Methods of Instruction **

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, media-based, hybrid or online course.

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

**VIII. Course Practices Required **

(To be completed by instructor)

**IX. Instructional Materials **

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

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.

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 **

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

**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.

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.