Exam 1, Thu Sep 22

first order equations: direction fields, theorem, Picard iteration

first order equations: linear, separable, exact, integrating factors

n-th order linear equations: fundamental sets of solutions, reduction of order (n=2)

Exam 2, Tue Oct 18

(n-th order linear equations)

possibly some topic from Exam 1

homogeneous equations with constant coefficients

non-homogeneous equations: method of undetermined coefficients

non-homogeneous equations: method of variation of parameters (n=2)

power series, series solution near an ordinary point, radius of convergence

Euler equations.

Exam 3, Thu Nov 10

possibly some topic from Exam 1 or 2

Series solution near a regular singular point

Laplace transform and its inverse, including discontinuous functions

solving differential equations using the Laplace transform

Exam 4, Tue Dec 13

possibly some topic from Exam 1, 2, or 3

systems of linear ODEs

two-point boundary value problems

Fourier series, even and odd functions

heat conduction problems (zero boundary conditions)