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MTH401 : Differential Equations

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Dr. Junaid Zaidi
University of Birmingham, England (UK)

Course Contents

Introduction to Differential equation Fundamentals of Differential equation Separable equations Homogeneous Differential equations Exact Differential equations Integrating factor technique First order Linear equations Bernoulli equations Applications of First order Differential equations Radioactive decay Applications of Non-linear equations Higher order linear differential equation Solution of Higher order linear differential equation Construction of a Second solution Homogeneous Linear equations with constant coefficients Method of undetermined coefficients(Superposition approach) Undetermined coefficient(Annihilator approach) Undetermined coefficient(Annihilator operator approach) Variation of Parameters Variation of Parameters method for higher order equations Applications of Second order differential equation Damped motion Forced motion Forced motion(examples) Differential equations with variable coefficients Cauchy-Euler equation (Alternative method of solution) Introduction to Power series Power series solution of a Differential equation Solution about Ordinary points Solutions about Singular points(regular and irregular singular points) Solutions about Singular points(Method of Frobenius) Bessel's Differential equation Legendre's Differential equation Systems of Linear Differential equations Systems of Linear Differential equations Systems of Linear First-order equations Introduction to Matrices The Eigenvalue problem Matrices and systems of Linear First-order equations Matrices and systems of linear First-order equations Homogeneous Linear systems Real and repeated Eigenvalues Non-Homogeneous system