MATH 251

    COURSE DESCRIPTION: Ordinary and Partial Differential Equations (4:4:0)
    First- and second-order equations; numerical methods; special functions;
    Laplace transform solutions; higher order equations; Fourier series,
    partial differential equations. Students who have passed Math 250 may
    only take a one credit section of this course.

    PREREQUISITE: Math 141

                                  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

    PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES
    Separation of Variables
    Fourier Series
    The Fourier Theorem
    Even and Odd Functions
    Solutions of Heat Conduction Problems
    The Wave Equation: Vibrations of an Elastic String
    Laplace's Equation
    

    
    AMK 6/21/95