- Exam 1, Tue Sep 22
- First order equations
- linear
- separable
- exact, integrating factors
- Picard iteration
- Second order linear equations
- reduction of order
- constant coefficients
- Euler equation
- method of variation of parameters
- method of undetermined coefficients (judicious guessing)
- Exam 2, Thu Oct 15
- possibly some topic from Exam 1
- series solution near an ordinary point
- matrices, exponential etA, eigenvalues and eigenvectors
- systems of first order linear ODEs
- Exam 3, Tue Nov 10
- possibly some topic from Exam 2
- systems of linear equations, row reduction
- matrix inverse and determinants via row reduction
- vector spaces, subspaces, span
- linear independence, bases, dimension
- linear transformations
- Exam 4, Wed Dec 9
- possibly some topic from Exam 3
- coordinates
- inner product spaces, Hermitian operators
- two-point boundary value problems
- Fourier series
- separation of variables, heat equation