Course Number and Title:
MAT 291 Ordinary Differential Equations
Prerequisites
Prerequisite: MAT 282 or MAT 283
Course Credits and Hours
4 credit(s)
4 lecture hours/week
1 lab hours/week
Course Description
This course examines solutions of ordinary differential equations of first and second order using qualitative, numeric, and analytic approaches. Mathematical modeling of real-life phenomena is studied.
Additional Materials
TI-84 Graphing Calculator
Core Course Performance Objectives (CCPOs)
- Classify, verify, and determine the existence and uniqueness of solutions to ordinary differential equations. (CCC 2, 6)
- Solve first-order differential equation including selected applications. (CCC 2, 6)
- Solve higher-order differential equation including selected applications. (CCC 2, 6)
- Use numerical techniques to solve ordinary differential equations. (CCC 2, 6)
- 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:
- Classify, verify, and determine the existence and uniqueness of solutions to ordinary differential equations.
- Classify differential equations by type, order, and linearity.
- Verify that given functions are solutions of defined differential equations.
- Examine initial value problems (IVP) to determine existence and uniqueness of solutions.
- Solve first-order differential equation including selected applications.
- Construct and examine direction fields to obtain the solution for a given differential equation.
- Solve first-order differential equations using separation of variables.
- Solve linear first-order differential equations using integrating factors.
- Solve first order exact differential equations.
- Construct and solve linear and nonlinear first-order differential equations from physical models.
- Solve higher-order differential equation including selected applications. (CCC 2, 6)
- Distinguish between solutions of homogeneous and nonhomogeneous higher-order differential equations.
- Determine linear independence or dependence of functions using the Wronskian.
- Solve linear homogeneous differential equation.
- Find the solution of non-homogenous differential equations by using the methods of undetermined coefficients and variation of parameters.
- Solve differential equations using Laplace transforms.
- Solve differential equations using power series.
- Solve initial-value problems (IVP) and boundary value problems (BVP).
- Solve applications of higher-order differential equations in natural systems
- Use numerical techniques to solve ordinary differential equations.
- Use Euler and Runge-Kutta methods to approximate the solution of simple differential equations.
- Calculate the errors in using the Euler and Runge-Kutta methods to estimate solutions of differential equations.
- Use a numerical solver employing the Euler and Runge-Kutta methods to solve differential equations.
- Solve systems of differential equations.
- Determine eigenvalues and eigenvectors of a matrix.
- Solve first order linear systems with constant coefficients with real eigenvalues, complex eigenvalues, or repeated eigenvalues.
- Solve applications with first order linear differential systems in physical systems.
Evaluation Criteria/Policies
The grade will be determined using the Delaware Tech grading system:
| 90-100 |
= |
A |
| 80-89 |
= |
B |
| 70-79 |
= |
C |
| 0-69 |
= |
F |
Students should refer to the
Catalog/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.
Final Course Grade
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)
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
Students in Need of Accommodations Due to a Disability
We value all individuals and provide an inclusive environment that fosters equity and student success. 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. The College's policy on accommodations for persons with disabilities can be found in the College's Guide to Requesting Academic Accommodations and/or Auxiliary Aids Students may also access the Guide and contact information for Disabilities Support Counselors through the Student Resources web page under Disabilities Support Services, or visit the campus Advising Center.