NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

 

 

TITLE OF COURSE:  Applied Differential Equations I (MTH 238)

 

DIVISION:  Mathematics, Science, and Technology

 

COURSE DESCRIPTION:  An introduction to numerical methods, qualitative behavior of first order differential equations, techniques for solving separable and linear equations analytically, and applications to various models (e.g. populations, motion, chemical mixtures, etc.); techniques for solving higher order linear differential equations with constant coefficients (general theory, undetermined coefficients, reduction of order and the method of variation of parameters), with emphasis on interpreting the behavior of the solutions, and applications to physical models whose governing equations are of higher order; the Laplace transform as a tool for the solution of initial value problems whose inhomogeneous terms are discontinuous.

 

HOURS: Credit:  3      Contact:  3       Lecture:  3        Clinical:  0        Lab:  0     

 

 

PRE-REQUISITE(S):  MTH 126

 

CO-REQUISITE(S):  MTH 227

 

REQUIRED TEXTBOOKS:  A First Course in Differential Equations with Modeling Applications, Eighth Edition, by Dennis G. Zill, Brooks/Cole, 2005.

 

SUPPLIES: A graphing calculator and access to Microsoft Excel software are highly recommended.

 

GENERAL EDUCATION OBJECTIVE:   All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

 

COURSE OBJECTIVE(S):  Upon successfully completing Applied Differential Equations I, the student should be able to:

  1. Define a differential equation, an initial value problem, and identify different types of differential equations.
  1. Define concept of mathematical model to represent a physical phenomenon or activity and generate a differential equation to solve applied problems.
  1. Develop and use methods such as separation of variables, substitutions, variation of parameters, reduction of order, and integrating factors to solve differential equations.
  1. Use existence and uniqueness theorems to determine whether solutions to differential equations exist and, if so, how many exist.
  1. Describe and use approximate solution techniques, including Euler’s and Runge-Kutta methods, for differential equations.
  1. Solve differential equations for applied problems involving population growth, radioactive decay, escape velocities of satellites, Newton’s Laws of motion, and electrical circuits.
  1. Use graphing techniques to determine the long-term behavior of solutions to differential equations.
  1. Solve second order differential equations with constant coefficients and selected nonlinear differential equations.
  1. Define the Laplace transform and use the concept to solve specific differential equations.

METHODS OF EVALUATION: 

 

  1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average.  Make-up examinations, as such, will not generally be given. 

                        

  1. Evaluation of General Educational Objectives:  Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations.  Performance on each course objective will be evaluated using appropriate problems from the final exam.  Results will be tallied for each course objective.

 

  1. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses.  The math department will meet once every five years to discuss findings and implement strategies to improve department and student performance.

OUTLINE OF COURSE TOPICS:

 

I.                    Introduction to Differential Equations

 

II.                 First-Order Differential Equations

 

III.               Modeling With First-Order Differential Equations

 

IV.              Higher Order Differential Equations

 

V.                 Series Solutions of Linear Equations

 

VI.              The Laplace Transform

 

VII.            Numerical Solutions of Ordinary Differential Equations

 

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

 

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

 

 

WITHDRAWAL POLICY:  A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings.  A student who withdraws by the date published in the schedule will receive a grade of “W” for the course.  This withdrawal is done only by student request.  The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal. 

 

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.