COURSE OUTLINE

MIDLANDS TECHNICAL COLLEGE

MAT 242 DIFFERENTIAL EQUATIONS

4.0 Credit Hours

COURSE DESCRIPTION: This course includes the following topics: solution of linear and elementary non-linear differential equations by standard methods with sufficient linear algebra to solve equations, applications, series, Laplace transforms and numerical methods.

TEXT: Elementary Differential Equations, Eighth Edition                                                                                                                                            by William E Boyce and Richard C. DiPrima                                                                                                                                                          John Wiley & Sons, Inc. 2005

PREREQUISITE: MAT 141

EQUIPMENT: Graphing Calculator, preferably TI-82 or TI-83

GRADING SCALE

    A 90 - 100        B 80 - 89        C 70 - 79        D 60 - 69        F Below 60

MATHEMATICS DEPARTMENT ATTENDANCE REGULATIONS

DEFINITIONS:

ABSENCE - Failure to be present for a scheduled meeting of the class or arriving for the class more than ten minutes after the scheduled time for the class to begin.

TARDY----- Arrival to class after the instructor has called the roll and before ten minutes past the time scheduled for the class to begin.

I. Absences are counted from the first day of classes.

II. Five absences are allowed for a class that meets three times per week and three absences are allowed for a class that meets two times per week.

III. Three tardies are considered as one absence. The student must meet with the instructor at the end of the class to which he has been late to have the absence changed to a tardy.

IV. There are no "excused" absences; all absences are counted regardless of the reason for the absence.

V. A student missing class time by leaving early will also be counted absent.

Please note: You are responsible for all material and announcements presented, whether you are present or absent.

Mathematics Department                                                                                                                                          Airport: 822-3357                                                                                                                                                                                                                                                                     Beltline:738-7689                                                                                                                                                                                             Revised 2/28/2007

MAT 242 COURSE OBJECTIVES

Students should be able to:

1. Solve first-order differential equations.

2. Use differential equations to develop a model for such processes as:

- motion in a gravitational field

- population growth

- vibrating systems

3. Solve second-order differential equations.

4. Use numerical methods to solve first-order differential equations.

5. Use Series methods and Laplace transforms.

6. Solve systems of differential equations.

7. Solve problems by identifying what information is available and relevant to the problem.

8. Solve problems by selecting or developing appropriate procedures and relations.

9. Solve problems by correctly applying the methods selected to the information available.

10. Solve problems by verifying the validity and appropriateness of the solution.

 

MAT 242 DIFFERENTIAL EQUATIONS
WEEK

TOPIC

 SECTION
1 Introduction  
      Some Basic Mathematical Models 1.1
      Solutions of Some Differential Equations 1.2
      Classification of Differential Equations 1.3
     
2     Historical Remarks 1.4
  First Order Differential Equations  
      Linear Equations: Methods of Integrating Factors 2.1
      Separable Equations 2.2
     
3     Modeling with First Order Equations 2.3
      Differences Between Linear and Nonlinear Equations 2.4
      Autonomous Equations and Population Dynamics 2.5
     
4     Exact Equations and Integrating Factors 2.6
      Numerical Approximations: Euler's Method 2.7
      The Existence and Uniqueness Theorem 2.8
     
5     TEST 1  
  Second Order Linear Equations  
      Homogenous Equations with Constant Coefficients 3.1
      Fundamental Solutions of Homogenous Equations 3.2
     
6     Linear Independence and the Wronskian 3.3
      Complex Roots of the Characteristic Equation 3.4
      Repeated Roots; Reduction of Order 3.5
     
7     Nonhomogenous Equations; Methods of Undetermined Coefficients 3.6
      Variation of Parameters 3.7
      TEST 2  
     
8 Higher Order Linear Equations  
      General Theory of nth Order Linear Equations 4.1
      Homogenous Equations with Constant Coefficients 4.2
      The Method of Undetermined Coefficients 4.3
      The Method of Variation of Parameters 4.4
     
9 Series Solutions of SecondOrder Linear Equations  
      Review of Power Series 5.1
      Series Solutions near an Ordinary Point, Part I 5.2
      Series Solutions near an Ordinary Point, Part II 5.3
      
10     Regular Single Points 5.4
      Euler Equations 5.5
      Series Solutions near a Regular Single Point 5.6
     
11     TEST 3  
  The Laplace Transform  
      Definition of the Laplace Transform 6.2
      Solution of Initial Value Problems 6.2
     
12     Step Functions 6.3
      Differential Equations with Discontinuous Forcing Functions 6.4
      TEST 4  
     
13 Systems of First Order Linear Equations  
      Introduction 7.1
      Review of Matrices 7.2
      Linear Algebraic Equations; Linear Independence; Eigenvalues, Eigenvectors 7.3
      Basic Theory of Systems of First Order Linear Equations 7.4
     
14     Homogeneous Linear Systems with Constant Coefficients 7.5
      Complex Eigenvales 7.6
      TEST 5  
     
  Comprehensive Final Examination