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• Preliminaries: Introduction and formulation, classification of differential equations Existence
• Existence and uniqueness of solutions
• Introduction of initial value and boundary value problems
• First order ordinary differential equations: Basic concepts, formation and solution of differential equations
• Separable variables, Exact Equations, Homogeneous Equations, Linear equations, integrating factors
• Some nonlinear first order equations with known solution, differential equations of Bernoulli and Ricaati type,Clairaut equation
• Modeling with first-order ODEs, Basic theory of systems of first order linear equations
• Homogeneous linear system with constant coefficients, Non homogeneous linear system,Second and higher order linear differential equations
• Mid Term Exam
• 9. Initial value and boundary value problems, Homogeneous and non-homogeneous equations
• 10. Superposition principle, homogeneous equations with constant coefficients, Linear independence and Wronskian
• Nonhomogeneous equations, undetermined coefficients method, variation of parameters, Cauchy-Euler equation
• Modeling. Sturm-Liouville problems: Introduction to eigen value problem, adjoint and self adjoint operators
• Self adjoint differential equations, eigen values and eigen functions, Sturm-Liouville (S-L) boundary value problems, regular and singular S-L problems, properties ofregular S-L problems
• 14. Series Solutions: Power series, ordinary and singular points, types of singular points ,Existence of power series solutions
• 15. Frobenius theorem, Existence of Frobenius series solutions, solutions about singular points
• 16. The Bessel, Modified Bessel, Legendre and Hermite equations and their solutions
• Final Term Exam
• Book
• Solution