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MTH701 : Advanced Differential Equations

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Dr. Junaid Zaidi

Course Contents

Higher Order Linear Differential Equations, Homogeneous Linear Equations with Constant Coefficients, Method of Undetermined Coefficients ( Superposition Approach), Method of Undetermined Coefficients (Annihilator Operator Approach), Variation of Parameters for Higher-Order Equations, Applications of Second Order Differential Equations, Differential Equations with Variable Coefficients, Cauchy-Euler Equation: Alternative Method of Solution, Power Series, Solution about Ordinary points, Solution about Singular Points, Bessel's Differential Equation, Legendre's Differential Equation, Systems of Linear Differential Equations, System of Linear First Order Equation, Eigen value Problem, Matrices and Systems of Linear First-Order Equations, Homogeneous Linear Systems, Linear and Repeated Eigen values, Non-Homogeneous System, Partial Differential Equations, Order,The Adomian decomposition method and convergence analysis, Adomian method for higher-order ordinary differential equations, Bratu type problems, Emden-Fowler equations and applications.