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
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EXERCISES
Excercise 1: Concept of Solutions, Separable Form, Geometric Interpretations
Excercise 2: Solutions of First Order ODE: Separable form, Exact Equations, Integrating Factors,
Bernoulli's equation; Orthogonal and Oblique Trajectories
Excercise 3: Nonhomogeneous First Order ODE, Existence and Uniqueness of IVP
Excercise 4: Second Order ODE: Solution of Second Order ODE, LI and LD Solutions, Wronskian
Excercise 5: Second Order ODE: Solution by Reduction of Order, IVP, Method of Undetermined Coefficients,
Method of Variation of Parameters
Excercise 6: Power Series Solution: Ordinary Points, Legendre Equation, Legendre Polynomials
Excercise 7: Frobenius Series Solution: Regular Singular Points, Bessel Equation, Bessel Functions,
Strum Comparison Theorem, Strum-Liouville BVP
Excercise 8: Laplace Transform
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