| Title | Summary |
|---|---|
| Second-Order Linear Equations: Reduction of Order | Paul's On-Line Notes on the order reduction method for second-order
homogeneous linear equations. Two examples are given --- one with constant coefficients and one with variable coefficients. |
| Second-Order Linear Equations: Fundamental Sets of Solutions | Paul's On-Line Notes on fundamental sets of solutions to second-order homogeneous
linear equations. Wronskians are introduced. |
| Second-Order Linear Equations: More on the Wronskian | Paul's On-Line Notes on the relationship between fundamental sets of solutions to second-order homogeneous linear equations, Wronskians, and the notion of linear independence. Abel's formula enters. |
| Higher-Order Linear Equations: Basic Concepts | Paul's On-Line Notes on higher-order homogeneous linear equations. They extend the topics covered above to higher-order equations. |
| Theory of General Second-Order Linear Homogeneous ODEs | Professor Mattuck (MIT video) intorduces linear operator notation and uses it to express the superposition property. The superposition property also holds for linear homogeneous equations of any order. This more general fact is shown in the notes by an argument the is essentially the same one used in this video. He goes on to introduce Wronskian and fundamental set of solutions. |
| Khan Academy: Second-Order Linear Homogeneous Differential Equations 1 | Khan Academy video showing the superposition property for second-order linear homogeneous equations with constant coefficients. The superposition property also holds for linear homogeneous equations of any order. This more general fact is shown in the text by an argument the is essentially the same one used in this video. |