Lectures related to Scalar Linear 2nd Order ODEs: Obtaining 2nd Solution

Covers second-order linear homogeneous differential equations and their solutions.

Homogeneous Solutions: Linear Independence

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

Linear Differential Equations

Covers the solution of linear differential equations of the first order, both homogeneous and inhomogeneous cases.

Advanced analysis II: second order linear ODEs

Explores second-order linear ODEs, solutions uniqueness, and linear independence.

Linear differential equations

Explores linear differential equations of order n, including homogeneous and inhomogeneous equations, solutions, and linear independence.

Scalar Linear Higher Order ODEs

Covers scalar linear higher order ODEs, focusing on properties of solutions and the superposition principle.

Linear Differential Equations: Solutions and Wronskian

Covers linear differential equations, focusing on solutions, the Wronskian, and methods for solving non-homogeneous equations.

Linear Differential Equations

Explores linear differential equations, including higher-order linear homogeneous equations and equations with constant coefficients.

Linearly Independent Solutions and Quadratic Equations

Explores linearly independent solutions in quadratic equations and the role of constants in trigonometric solutions.

General Solutions of Differential Equations

Explores general solutions of differential equations, emphasizing homogeneous and inhomogeneous equations and the process of finding solutions.

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.

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.

Second Order Equations: Wronskian and Linear Independence

Explores the concept of linear independence in second-order equations using the Wronskian.

General Solution of Inhomogeneous ED

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

Linear Second Order ODEs

Covers the solution of linear second order ODEs with constant coefficients and explores the method of variation of parameters.

Linear Differential Equations

Covers linear differential equations of order n with constant coefficients and how to find their general solutions.

Solutions of Homogeneous Linear Differential Equations

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

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

Linear Homogeneous Second Order Equations

Covers linear homogeneous second order differential equations and their solutions, including the concept of the Wronskian.

Linear Independence and Basis

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