MA 380 - Advanced Differential Equations

• 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

• 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

• 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)