MATH 250
    
    COURSE DESCRIPTION: Ordinary Differential Equations (3:3:0) First- and
    second-order equations; numerical methods; special functions; Laplace
    transform solutions; higher order equations. Students who have passed
    Math 251 may not schedule this course for credit.
    
    PREREaUISITE: Math 141 GQ.

                                  TOPICS
    
    INTRODUCTION
    Classification of Differential Equations

    FIRST ORDER DIFFERENTIAL EQUATIONS
    Linear Equations
    Further Discussion of Linear Equations
    Separable Equations
    Applications of First Order Linear Equations
    Population Dynamics and Some Related Problems
    Problems in Mechanics
    Exact Equations and Integrating Factors
    
    SECOND ORDER LINEAR EQUATIONS
    Homogeneous Equations with Constant Coefficients
    Fundamental Solutions of Linear Homogeneous Equations
    Linear Independence and the Wronskian
    Complex Roots of the Characteristic Equations
    Repeated Roots; Reduction of Order
    Nonhomogeneous Equations; Method of Undetermined Coefficients
    Variation of Parameters
    Mechanical and Electrical Vibrations
    Forced Vibrations

    HIGHER ORDER LINEAR EQUATIONS
    General Theory of nth Order Linear Equations
    Homogeneous Equations with Constant Coefficients
    The Method of Undetermined Coefficients

    SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS
    Series Solutions near an Ordinary Point

    THE LAPLACE TRANSFORM
    Definition of the Laplace Transform
    Solution of Initial Value Problems
    Step Functions
    Differential Equations with Discontinuous Forcing Functions
    Impulse Functions

    NUMERICAL METHODS
    The Euler or Tangent Line Method
    Errors in Numerical Procedures
    Improvements on the Euler Method
    The Runge-Kutta Method
    

    
    AMK 6/21/95