Ordinary Differential Equation Notes by S. Ghorai

This note
covers the following topics: Geometrical Interpretation of ODE, Solution of
First Order ODE, Linear Equations, Orthogonal Trajectories, Existence and
Uniqueness Theorems, Picard's Iteration, Numerical Methods, Second Order Linear
ODE, Homogeneous Linear ODE with Constant Coefficients, Non-homogeneous Linear
ODE, Method of Undetermined Coefficients, Non-homogeneous Linear ODE, Method of
Variation of Parameters, Euler-Cauchy Equations, Power Series Solutions:
Ordinary Points, Legendre Equation, Legendre Polynomials, Frobenius Series
Solution, Regular Singular Point, Bessle Equation, Bessel Function, Strum
Comparison Theorem, Orthogonality of Bessel Function, Laplace Transform, Inverse
Laplace Transform, Existence and Properties of Laplace Transform, Unit step
function, Laplace Transform of Derivatives and Integration, Derivative and
Integration of Laplace Transform, Laplace Transform of Periodic Functions,
Convolution, Applications.

**Author(s):** S. Ghorai

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