Linear Homogeneous Second Order Equations

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Linear Differential Equations

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

General Solution of Inhomogeneous ED

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

Semi-groups of Contractions

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Linear Differential Equations

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

Linear Differential Equations: Solution Methods

Covers solution methods for linear differential equations of second order with constant coefficients.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Homogeneous Linear Second-Order Differential Equations

Covers the solution of homogeneous linear second-order differential equations with constant coefficients and explores various cases of real and complex roots.

Linearly Independent Solutions and Quadratic Equations

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

Linear Differential Equations

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

Homogeneous Equations: Advanced Analysis II

Explores second-order linear scalar homogeneous equations in advanced analysis II.