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. Corequisite 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
ProgramApplicable Courses – This course is required 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. CollegeWide Outcomes
CollegeWide 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 higherorder problemsolving 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. InitialValue Problems

IIa. Direction Fields, Phase Portraits, and Stability

IIb. Separable Variables

IIc. Linear Equations

IId. Mathematical Models

IIe. Numerical Methods

IIIa. Higherorder Linear Equations

IIIb. Homogenenous Linear Equations with Constant Coefficients

IIIc. Nonhomogeneous Linear Equations

IIId. CauchyEuler Equation

IIIe. Mathematical Models

IIIf. BoundaryValue 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. Corequisite 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. ProgramApplicable Courses – This course is required 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. CollegeWide Outcomes
CollegeWide 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 higherorder problemsolving 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. InitialValue Problems

IIa. Direction Fields, Phase Portraits, and Stability

IIb. Separable Variables

IIc. Linear Equations

IId. Mathematical Models

IIe. Numerical Methods

IIIa. Higherorder Linear Equations

IIIb. Homogenenous Linear Equations with Constant Coefficients

IIIc. Nonhomogeneous Linear Equations

IIId. CauchyEuler Equation

IIIe. Mathematical Models

IIIf. BoundaryValue 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
