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• Week 01: Introduction to differential equations: preliminaries and classification of differential equations
• Week 02: Verification of solution, existence of unique solutions
• Week 03: Introduction to initial value problems  Differential equations as mathematical models
• Week 04: First order ordinary differential equations: Basic concepts, formation and solution of differential equations
• Week 05: Separable equations, Linear equations , integrating factors, Exact Equations
• Week 06: Solution of some nonlinear first order DEs by substitution, Homogeneous Equations, Bernoulli equation, Ricaati’s equation and Clairaut equation
• Week 07: Modeling with first-order ODEs: Linear models, Nonlinear models
• Week 08: Higher order differential equations
• Week 09: Mid Term Examination
• Week 10: Reduction of order, homogeneous equations with constant coefficients
• Week 11: Nonhomogeneous equations, undetermined coefficients method, Superposition principle, Annihilator approach, variation of parameters, Cauchy-Euler equation
• Week 12: Solving system of linear DEs by elimination, solution of nonlinear DEs
• Week 13: Series Solutions: Power series, ordinary and singular points, Existence of power series solutions
• Week 14: Solutions about singular points, types of singular points, Frobenius theorem, Existence of Frobenius series solutions
• Week 15: Special functions, The Bessel, Modified Bessel, Legendre and Hermite equations and their solutions.  Sturm-Liouville problems, eigen values, adjoint and self adjoint
• Week 16: Self adjoint differential equations, eigen values and eigen functions, Sturm-Liouville (S-L) boundary value problems, regular and singular S-L problems and properties
• Week 17: Final Term Exam