Lecture Notes : ODE

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MOTIVATION

Lecture 1: Introduction, Concept of Solutions, Applications

Lecture 2: Geometrical Interpretation of ODE

Lecture 3: Solution of First Order ODE

Lecture 4: Linear Equations, Orthogonal Trajectories

Lecture 5: Existence and Uniqueness Theorems, Picard's Iteration

Lecture 6: Numerical Methods

Lecture 7: Second Order Linear ODE

Lecture 8: Homogeneous Linear ODE with Constant Coefficients

Lecture 9: Non-homogeneous Linear ODE, Method of Undetermined Coefficients

Lecture 10: Non-homogeneous Linear ODE, Method of Variation of Parameters

Lecture 11: Euler-Cauchy Equations

Lecture 12: Power Series Solutions: Ordinary Points

Lecture 13: Legendre Equation, Legendre Polynomials

Lecture 14: Frobenius Series Solution, Regular Singular Point

Lecture 15: Bessle Equation, Bessel Function

Lecture 16: Strum Comparison Theorem, Orthogonality of Bessel Function

Lecture 17: Laplace Transform, inverse Laplace Transform, Existence and Properties of Laplace Transform

Lecture 18: Unit step function, Laplace Transform of Derivatives and Integration, Derivative and Integration of Laplace Transform

Lecture 19: Laplace Transform of Periodic Functions, Convolution, Applications