# MA 238

## MA 238 Applied Differential Equations

### Course Description and Goals

This course provides an elementary introduction to the techniques and necessary theory for solving the basic differential equations usually encountered by beginning science and engineering students. General topics include

• analytical and graphical methods for solving and analyzing first-order differential equations
• Euler's numerical method
• the basic theory of higher-order, linear differential equations, with major emphasis on equations with constant coefficients
• variation of parameters
• the Laplace transform as a tool for solving differential equations.

Course goals include

• a basic understanding the special language, notation, and point of view of differential equations, and the importance of differential equations in the modeling of many physical laws and processes.
• the ability to solve basic differential equations
• a basic understanding of differential equations from contrasting but complementary points of view: algebraic, graphical, numerical, and procedural
• reinforcement of the concepts and techniques learned in calculus
• a basic understanding of some classical problems and processes, such as spring mass systems, and electrical circuits
• an improved ability to read, write, speak, and think in mathematical terms

### Alabama General Studies Curriculum

MA 238 is an AGSC approved course. The standard AGSC number is Math 238.

### Prerequisites

MA 172 and MA 201 (co-requisite)

### Credit Hours

3 Semester Hours

This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework, Maple assignments, quizzes, and a comprehensive final exam.

### Course Materials

• Text: Preliminary version of Ordinary Differential Equations, by Kenneth Howell. This is available in the University Bookstore and online at http://www.uah.edu/howell/DEtext/index.htm.
• Maple 12 is the computer algebra system recommended for this course.

Sections of Text Covered:

• Part I, Basics: Chapters 1 and 2
• Part II, First-Order Equations: Chapters 3, 4, 5, 6, 8, 9 & 10
• Part III, Second- and Higher-Order Equations: Chapters 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22 & 23
• Part IV, The Laplace Transform: Chapters 24, 25, 26, 27, 28 & 29