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
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: