Ordinary Differential Equations
A 26-module path through ordinary differential equations, in study order from foundations to the frontier.
Modules
- First-Order ODEs and Direction Fields
- Separable Equations
- Linear First-Order Equations
- Exact Equations
- Integrating Factors for Non-Exact Equations
- Existence and Uniqueness (Picard-Lindelof)
- Second-Order Linear Equations
- The Wronskian and Linear Independence
- Fundamental Sets and General Solutions
- Homogeneous Equations with Constant Coefficients
- Complex and Repeated Roots
- Method of Undetermined Coefficients
- Variation of Parameters
- Higher-Order Linear Equations
- Series Solutions Near Ordinary Points
- Regular Singular Points and Frobenius
- The Laplace Transform: Definition and Existence
- Transforms of Derivatives and IVPs
- Inverse Laplace Transform and Partial Fractions
- Step Functions, Impulses, and Convolution
- Systems of First-Order Linear ODEs
- Eigenvalue Method for Linear Systems
- Complex and Repeated Eigenvalues
- The Matrix Exponential
- Phase Portraits for Linear Systems
- Stability and Classification of Equilibria