I. General Information
1. Course Title:
Differential Equations
2. Course Prefix & Number:
MATH 2459
3. Course Credits and Contact Hours:
Credits: 4
Lecture Hours: 4
Lab Hours: 0
4. Course Description:
Existence and uniqueness theorem. Ordinary first order differential equations, linear equations of higher orders, and initial value problems. Systems of differential equations, LaPlace transforms, and power series methods applications.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 2459 - Differential Equations
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1478 | Calculus II | 5 cr. |
9. Co-requisite Courses:
MATH 2459 - Differential Equations
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency - similar course from other regional institutions:
|
Name of Institution
|
Course Number and Title
|
Credits
|
|
St. Cloud State University
|
MATH 325. Differential Equations
|
3
|
|
Bemidji State University
|
MATH 2490 DIFFERENTIAL EQUATIONS
|
4
|
III. Course Purpose
Program-Applicable Courses – This course fulfills a requirement for the following program(s):
|
Name of Program(s)
|
Program Type
|
|
Engineering
|
AS
|
MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning
IV. Learning Outcomes
1. College-Wide Outcomes
| College-Wide Outcomes/Competencies |
Students will be able to: |
| Assess alternative solutions to a problem |
Examine differing methods in solving problems, e.g. solving a differential equation with initial values using undetermined coefficients or Laplace transforms. |
| Apply abstract ideas to concrete situations |
Apply concepts and methods to solve application problems. |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
|
Clearly express mathematical ideas in writing.
|
|
Explain what constitutes a valid mathematical argument.
|
|
Apply higher-order problem-solving strategies.
|
|
Apply appropriate technology.
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
Ia. Definitions and terminology
|
|
Ib. Initial-Value Problems
|
|
IIa. Direction Fields, Phase Portraits, and Stability
|
|
IIb. Separable Variables
|
|
IIc. Linear Equations
|
|
IId. Mathematical Models
|
|
IIe. Numerical Methods
|
|
IIIa. Higher-order Linear Equations
|
|
IIIb. Homogenenous Linear Equations with Constant Coefficients
|
|
IIIc. Nonhomogeneous Linear Equations
|
|
IIId. Cauchy-Euler Equation
|
|
IIIe. Mathematical Models
|
|
IIIf. Boundary-Value Problems
|
|
IIIg. Systems of Differential Equations – Elimination Method
|
|
IVa. Linear Systems
|
|
IVb. Homogeneous Linear Systems with Constant Coefficients
|
|
Va. Definition of the Laplace Transform
|
|
Vb. Translation Theorems
|
|
Vc. Derivative of a Transform, Transform of an Integral.
|
|
Vd. Periodic Functions
|
|
Ve. Dirac Delta Function
|
I. General Information
1. Course Title:
Differential Equations
2. Course Prefix & Number:
MATH 2459
3. Course Credits and Contact Hours:
Credits: 4
Lecture Hours: 4
Lab Hours: 0
4. Course Description:
Existence and uniqueness theorem. Ordinary first order differential equations, linear equations of higher orders, and initial value problems. Systems of differential equations, LaPlace transforms, and power series methods applications.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 2459 - Differential Equations
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1478 | Calculus II | 5 cr. |
9. Co-requisite Courses:
MATH 2459 - Differential Equations
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency - similar course from other regional institutions:
|
Name of Institution
|
Course Number and Title
|
Credits
|
|
St. Cloud State University
|
MATH 325. Differential Equations
|
3
|
|
Bemidji State University
|
MATH 2490 DIFFERENTIAL EQUATIONS
|
4
|
III. Course Purpose
1. Program-Applicable Courses – This course fulfills a requirement for the following program(s):
|
Name of Program(s)
|
Program Type
|
|
Engineering
|
AS
|
2. MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning
IV. Learning Outcomes
1. College-Wide Outcomes
| College-Wide Outcomes/Competencies |
Students will be able to: |
| Apply abstract ideas to concrete situations |
Apply concepts and methods to solve application problems. |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
|
Clearly express mathematical ideas in writing.
|
|
Explain what constitutes a valid mathematical argument.
|
|
Apply higher-order problem-solving strategies.
|
|
Apply appropriate technology.
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
Ia. Definitions and terminology
|
|
Ib. Initial-Value Problems
|
|
IIa. Direction Fields, Phase Portraits, and Stability
|
|
IIb. Separable Variables
|
|
IIc. Linear Equations
|
|
IId. Mathematical Models
|
|
IIe. Numerical Methods
|
|
IIIa. Higher-order Linear Equations
|
|
IIIb. Homogenenous Linear Equations with Constant Coefficients
|
|
IIIc. Nonhomogeneous Linear Equations
|
|
IIId. Cauchy-Euler Equation
|
|
IIIe. Mathematical Models
|
|
IIIf. Boundary-Value Problems
|
|
IIIg. Systems of Differential Equations – Elimination Method
|
|
IVa. Linear Systems
|
|
IVb. Homogeneous Linear Systems with Constant Coefficients
|
|
Va. Definition of the Laplace Transform
|
|
Vb. Translation Theorems
|
|
Vc. Derivative of a Transform, Transform of an Integral.
|
|
Vd. Periodic Functions
|
|
Ve. Dirac Delta Function
|