MATH 626 Differential Equations
Catalog Description:
This is a course in ordinary and partial differential equations including topics such as separating variables, linear first and higher order differential equations and applications. In addition to many applications, the course includes an examination of the theory supporting various techniques for solution. Computer software is used as needed.
Prerequisites: Math 621, Selected Topics in Advanced Calculus II.
Student Learning
Outcomes and Course Goals:
A. To serve as an introduction to differential equations.
B. To utilize a student's background in Calculus in solving differential equations.
C. To illustrate several of the many applications of differential equations.
Instructional
Procedures:
A. Lecture/Discussion
B.
C. Computer projects
Course Content:
A. Introduction
1. Classification of Differential Equations
2. History
B. First Order Differential Equations
1. Linear Equations
(1). Separable Equations
(2). Exact Equations
(3). Non Exact Equations and Integrating Factors
(4). Homogeneous Equations
2. Existence and Uniqueness Theorem
3. Applications of First Order Linear Equations
C. Second Order Linear Equations
1. Introduction
2. Fundamental Solutions of the Homogeneous Equation
3. Linear Independence
4. Reduction of Order
5. Homogeneous Equations with Constant Coefficients
6. Nonhomogeneous Equations
(1). Method of Undetermined Coefficients
(2). Method of Variation of Parameters
D. Higher Order Linear Equations
1. Introduction
2. General Theory of nth Order Linear Equations
3. Homogeneous Equations with Constant Coefficients
4. Method of Undetermined Coefficients
5. Method of Variation of Parameters
Bibliography:
a. Required Text: Zill, Dennis G., A First Course in
Differential Equations, 7th Ed., PWS-Kent,
b. Additional Required
Boyce, William E., Elementary Differential Equations and Boundary Value Problems, 8th Ed., John Wiley & Sons, New York, 2005. *
Braun,
M., Differential Equations and Their Applications, 4th Ed.,