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Jul 27, 2024
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MA 380 - Advanced Differential Equations3 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 (10 classes)
• Solution of linear differential equations near ordinary points and regular singular points (10 classes)
• Solution of systems of differential equations using matrix methods (7 classes)
• Exams (2 classes)
Coordinator
Ronald Jorgensen
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