Exam 1, Thu Feb 6

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

Exam 2, Thu Mar 6

(n-th order linear equations)

possibly some topic from Exam 1

reduction of order (n=2)

homogeneous equations with constant coefficients

non-homogeneous equations: method of undetermined coefficients

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

series solution near an ordinary point

Exam 3, Thu Apr 10

possibly some topic from Exam 1 or 2

Euler equations, series solution near a regular singular point

Laplace transform and its inverse, including discontinuous functions

solving differential equations using the Laplace transform

systems of linear ODEs: solution via the exponential of a matrix

Exam 4, Mon May 12

possibly some topic from Exam 1, 2, or 3

systems of linear ODEs

two-point boundary value problems

Fourier series, even and odd functions

separation of variables, heat conduction problems