Ordinary Differential Equations
I. Course Prefix/Number: MAT 262
Course Name: Ordinary Differential Equations
Credits: 3 (3 lecture; 0 lab)
III. Course (Catalog) Description
IV. Learning Objectives
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
• 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
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
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
Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
IX. Instructional Materials
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
XI. Other Course Information
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 the Learning Center. 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.