**MTH 279 Syllabus**

**Division**: Arts and Sciences Date: January, 2014

**Curricula in Which Course is
Taught**:

**Course Number and Title**: MTH 279, Ordinary Differential Equations

**Credit Hours**: 4 **Hours/Wk Lecture**: **Hours/Wk Lab**: **Lec****/Lab Comb**:

**I.
****Catalog Description: **Introduces
ordinary differential equations. Includes first order differential equations,
second and higher order ordinary differential equations with application.
Designed for mathematical, physical, and engineering science programs.
Prerequisite: MTH 274 or equivalent. Lecture 4 hours per week.

** **

**II.
****Relationship of the course to
curricula objectives in which it is taught:
**

This
course is required in the engineering transfer program and will count as a math
elective in other transfer programs.

Applications
focus on techniques for solving differential equations that provide realistic
models of a great variety of systems in essentially all engineering and
scientific disciplines.

**III.
****Required background**:

MTH 274 or
equivalent

**IV.
****Course Content**:

1.
Solutions and Classification of
Differentiation Equations

2.
First Order Differential
Equations

3.
Second Order Linear Equations

4.
Higher Order Linear Equations

5.
Euler Equations

6.
The Laplace Transform

7.
Systems of First Order Linear
Equations

8.
Numeral Methods – The Euler or
Tangent Line Method, Improvements on the Euler Method, and The Runge-Kutta Method

**V.
****Learner Outcomes**

Upon completion of the course, students are expected to be able
to:

A. understand the basic concepts in differential equations
such as: existence and uniqueness of solutions, non-linearity, continuous
dependence of solutions on the initial conditions and the parameters of the
equation, long-term behavior, and stability

B. master the
mathematical techniques required to solve ordinary differential equations

C. pose
physical problems and write them in the form of mathematical equations

D. determine which methods are suitable for solving equations
arising from various applications, and then use those methods to solve the equations

E. evaluate and interpret the mathematical results obtained in
the context of the physical process being studied and the model used

**VI. Evaluation**

Students
will be evaluated by some combination of quizzes, tests, homework and exams as
defined by faculty**. Students will use calculators only after
demonstrating mastery of essential deductive skills without them.**

**VI.
****This course supports the following objectives:**

** **

**DCC Educational Objectives:
**

Critical
Thinking

Quantitative Reasoning

Scientific
Reasoning