Solutions of Homogeneous Linear Differential Equations

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.

Linear Differential Equations: Solution Methods

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

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Homogeneous Solutions: Linear Independence

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

Linear Independence and Basis

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