MP3 · Ordinary differential equations
A 20-module path through mp3 · ordinary differential equations, in study order from foundations to the frontier.
Modules
- First-Order Ordinary Differential Equations
- Integrating Factors and Exact Equations
- Existence and Uniqueness Theorems for ODEs
- Linear Second-Order ODEs
- The Wronskian and Linear Independence
- Reduction of Order
- Variation of Parameters
- Ordinary and Singular Points
- Power Series Solutions
- The Method of Frobenius
- Indicial Equation and Exponents
- Two-Point Boundary-Value Problems
- Sturm-Liouville Theory
- Sturm-Liouville Eigenvalues and Oscillation Theorems
- Eigenfunction Expansions and Completeness
- Self-Adjointness and Boundary Conditions
- Green's Functions for Ordinary Differential Equations
- Green's Function Construction by Matching
- Spectral Representation of Green's Functions
- Modified Green's Functions and Solvability