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• WEEK-1: Preliminaries: Introduction and formulation, classification of differential equations Existence
• WEEK-2: Existence and uniqueness of solutions, Introduction of initial value and boundary value problems
• WEEK-3: First order ordinary differential equations: Basic concepts, formation and solution of differential equations
• WEEK-4: Separable variables, Exact Equations, Homogeneous Equations.
• WEEK-5: Linear equations, integrating factors Some nonlinear first order equations with known solution, differential equations of Bernoulli and Ricati type,Clairaut equation
• WEEK-6: Modeling with first-order ODEs, Basic theory of systems of first order linear equations Homogeneous linear system with constant coefficients.
• WEEK-7: Basic Homogeneous linear system Non homogeneous linear system,Second and higher order linear differential equations
• WEEK-8: Initial value and boundary value problems, Homogeneous and non-homogeneous equations.
• WEEK-9: MID TERM EXAM
• WEEK-10: Superposition principle, homogeneous equations with constant coefficients, Linear independence and Wronskian
• WEEK-11: Nonhomogeneous equations, undetermined coefficients method, variation of parameters, Cauchy-Euler equation
• WEEK-12: Modeling. Sturm-Liouville problems: Introduction to eigen value problem, adjoint and self adjoint operators Self adjoint differential equations,
• WEEK-13: eigen values and eigen functions, Sturm-Liouville (S-L) boundary value problems, regular and singular S-L problems, properties ofregular S-L problems
• WEEK-14: regular and singular S-L problems, properties ofregular S-L problems
• WEEK-15: Series Solutions: Power series, ordinary and singular points, types of singular points ,Existence of power series solutions
• WEEK-16: Frobenius theorem, Existence of Frobenius series solutions, solutions about singular points
• WEEK-17: The Bessel, Modified Bessel, Legendre and Hermite equations and their solutions.
• WEEK-18 Final examination