Frobenius Method: General Case of Regular Singular Point

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Frobenius Method: Regular Singular Points

Explores the Frobenius method for solving ODEs at regular singular points.

Frobenius Method: Introduction

Introduces the Frobenius method for solving second-order linear ODEs around ordinary points.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Bessel Equation: Second Frobenius Series Solution

Explores the Bessel equation, deriving solutions and investigating the existence of a second Frobenius series solution.

Homogeneous Solutions: Linear Independence

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Solutions of Homogeneous Linear Differential Equations

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Scalar Linear Higher Order ODEs: Properties and Solutions

Explores properties and solutions of scalar linear higher order ODEs with x-dependent coefficients and constant coefficients.

General Solution of Homogeneous Second Order Linear Differential Equations

Covers the general solution of homogeneous second-order linear differential equations with constant coefficients and the concept of linear independence of solutions.

Linear Differential Equations

Covers second-order linear differential equations and their solutions, including the method of variation of constants.

General Solution of Inhomogeneous ED

Covers the general solution of inhomogeneous differential equations and explores linear dependence, uniqueness theorems, and second-order equations.