Mathematics
MATH 252
Differential Equations (50) 5 Cr. Hrs.


Course Description
Topics covered in this course include first order differential equations, second order linear equations, series solutions of second order linear equations, higher order linear equations, Laplace transform, systems of first order linear equations, numerical methods and qualitative theory of differential equations.
Prerequisites
(A requirement that must be completed before taking this course.)
Course Competencies
Upon successful completion of the course, the student should be able to:
 Model a mechanical oscillator.
 Model a series or parallel electrical circuit of the RLC (resistor, inductor, capacitor) type.
 Model one population in conditions of natural growth or decay, logistic growth, explosion, or extinction.
 Model two populations in conditions of predation or competition.
 Sketch graphical solutions of a firstorder differential equation by hand using the slope field.
 Determine the general solution of a simple firstorder differential equation using such techniques as separation of variables, integrating factors, and substitution methods.
 Compute the approximate solution of a firstorder initialvalue differential equation using a numerical method (Euler, RungeKutta, etc.) by hand or with a calculating device.
 Determine the general solution of a homogeneous constantcoefficient linear differential equation by using the Characteristic Polynomial method.
 Determine the general solution of a nonhomogeneous constantcoefficient linear differential equation by using the Undetermined Coefficients or Variation of Parameters method.
 Determine the general solution of a system of linear differential equations by finding its real or complex eigenvalues and eigenvectors.
 Identify graphically the location, type, and stability of all critical points in a given phaseplane diagram.
 Determine analytically the location, type, and stability of all critical points by finding the eigenvalues of the linearized system.
 Determine the Laplace transform of various simple functions by hand.
 Determine the Laplace transform of various continuous, piecewisecontinuous, or periodic functions with the aid of a table.
 Determine the inverse Laplace transform of various functions with the aid of a table.
 Solve differential equations by the Laplace transform method.
 Determine power series solutions of a differential equation and their radii of convergence.
Course Schedule
 252  143110  Differential Equations   5  Schwartz R  $12.00  0/31/3  Closed  M T W R  01:15PM02:22PM  BTC165 

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