# MAT 291 Ordinary Differential Equations

Campus Location:
Georgetown, Dover, Stanton
Effective Date:
2021-51
Prerequisite:
MAT 282 or MAT 283
Co-Requisites:

None

Course Credits and Hours:
4.00 credits
4.00 lecture hours/week
1.00 lab hours/week
Course Description:

This course examines solutions and applications of ordinary differential equations and systems of these equations. Solution and applications of initial value problems and boundary value problems are covered. Topics include Laplace transform, the phase plane, and series solutions of differential equations. Mathematical modeling of natural phenomena is also studied.

Required Text(s):

Obtain current textbook information by viewing the campus bookstore online or visit a campus bookstore. Check your course schedule for the course number and section.

TI-84 Graphing Calculator

Schedule Type:
Classroom Course
Disclaimer:

None

Core Course Performance Objectives (CCPOs):
1. Classify, verify, and determine the existence and uniqueness of solutions to ordinary differential equations. (CCC 2, 6)
2. Solve first-order differential equation including selected applications. (CCC 2, 6)
3. Solve higher-order differential equation including selected applications. (CCC 2, 6)
4. Use numerical techniques to solve ordinary differential equations. (CCC 2, 6)
5. Solve systems of differential equations. (CCC 2, 6)

See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.

Measurable Performance Objectives (MPOs):

Upon completion of this course, the student will:

1. Classify, verify, and determine the existence and uniqueness of solutions to ordinary differential equations.
1. Classify differential equations by type, order, and linearity.
2. Verify that given functions are solutions of defined differential equations.
3. Examine initial value problems (IVP) to determine existence and uniqueness of solutions.
2. Solve first-order differential equation including selected applications.
1. Construct and examine direction fields to obtain the solution for a given differential equation.
2. Solve first-order differential equations using separation of variables.
3. Solve linear first-order differential equations using integrating factors.
4. Solve first order exact differential equations.
5. Construct and solve linear and nonlinear first-order differential equations from physical models.
3. Solve higher-order differential equation including selected applications. (CCC 2, 6)
1. Distinguish between solutions of homogeneous and nonhomogeneous higher-order differential equations.
2. Determine linear independence or dependence of functions using the Wronskian.
3. Solve linear homogeneous differential equation.
4. Find the solution of non-homogenous differential equations by using the methods of undetermined coefficients and variation of parameters.
5. Solve differential equations using Laplace transforms.
6. Solve differential equations using power series.
7. Solve initial-value problems (IVP) and boundary value problems (BVP).
8. Solve applications of higher-order differential equations in natural systems
4. Use numerical techniques to solve ordinary differential equations.
1. Use Euler and Runge-Kutta methods to approximate the solution of simple differential equations.
2. Calculate the errors in using the Euler and Runge-Kutta methods to estimate solutions of differential equations.
3. Use a numerical solver employing the Euler and Runge-Kutta methods to solve differential equations.
5. Solve systems of differential equations.
1. Determine eigenvalues and eigenvectors of a matrix.
2. Solve first order linear systems with constant coefficients with real eigenvalues, complex eigenvalues, or repeated eigenvalues.
3. Solve applications with first order linear differential systems in physical systems.
Evaluation Criteria/Policies:

90 100 = A
80 89 = B
70 79 = C
0 69 = F

Students should refer to the Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.

Calculated using the following weighted average

 Evaluation Measure Percentage of final grade 4 Tests (summative) (equally weighted) 75% Homework (formative) 15% Programming Assignments (formative) 5% Formative Assessments 5% TOTAL 100%
Core Curriculum Competencies (CCCs are the competencies every graduate will develop):
1. Apply clear and effective communication skills.
2. Use critical thinking to solve problems.
3. Collaborate to achieve a common goal.
4. Demonstrate professional and ethical conduct.
5. Use information literacy for effective vocational and/or academic research.
6. Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
Program Graduate Competencies (PGCs are the competencies every graduate will develop specific to his or her major):

None

Disabilities Support Statement:

The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.

Minimum Technology Requirements:
Minimum technology requirements for online, hybrid, video conferencing and web conferencing courses.