- Exam 1, Tue Sep 20
- 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
- Exam 2, Thu Oct 13
- possibly some topic from Exam 1
- method of undetermined coefficients (judicious guessing)
- series solution near an ordinary point
- solving systems of first order linear ODEs via matrix exponential etA
- Exam 3, Thu Nov 3
- possibly some topic from Exam 2
- eigenvalues and eigenvectors, systems of first order linear ODEs
- Row reduction and applications
- systems of linear equations, matrix inverse, determinants
- linear (in)dependence and spanning properties of vectors in ℝn
- Exam 4, Thu Dec 8
- possibly some topic from Exam 3
- vector spaces, subspaces, span, linear independence, bases, dimension
- linear transformations, coordinates
- two-point boundary value problems
- Fourier series
- separation of variables, heat equation (including inhomogeneous boundary conditions)