Feb 25, 2024  
2018-2019 Undergraduate Academic Catalog 
    
2018-2019 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 380 - Advanced Differential Equations

3 lecture hours 0 lab hours 3 credits
Course Description
This course presents the student with more powerful methods of solving differential equations. Topics include matrix methods for solution of systems of linear differential equations, open-form solutions of linear differential equations with variable coefficients using infinite series (including the method of Frobenius), and additional Laplace transform methods. (prereq: MA 235 , MA 232 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Solve some linear systems of ordinary differential equations by Laplace transforms and differential operator methods including the Heavyside function, convolutions, Gamma functions, and periodic functions
  • Solve some linear ordinary differential equations with variable coefficients near an ordinary point
  • Solve some linear ordinary differential equations with variable coefficients near a regular singular point
  • Solve systems of linear differential equations using matrix methods

Prerequisites by Topic
  • Convergence status and interval of convergence of infinite series
  • Power series manipulations using differentiation and integration
  • Using Maclaurin and Taylor series to approximate functions
  • Solution of higher-order linear homogeneous differential equations having constant coefficients
  • Solution of non-homogeneous linear differential equations having constant coefficients using the methods of undetermined coefficients and variation of parameters
  • Solution of linear differential equations using Laplace transforms
  • Matrix operations such as row manipulations, matrix inversion, and solution of a system of equations using matrices

Course Topics
  • Solution of differential equations using Laplace transforms
  • Solution of linear differential equations near ordinary points and regular singular points
  • Solution of systems of differential equations using matrix methods

Coordinator
Bruce O’Neill



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