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