ACM 95b/100b Winter 2004.	Sterl Phinney	2/2/2004

What about ordinary differential equations is examinable on midterm:

Classification of DEs: order?, nonlinear or not? homogeneous or not? 
  IVP or BVP?
Solutions: What is a general solution vs a particular solution (aka integral 
  curve)?
Existence and uniqueness. Recognise why solutions sometimes exist only over
  finite intervals, and why there can be nonuniqueness.
Euler method -Euler polygonal approximation to solution of a DE.
Separable nonlinear ODEs
linear first order ODEs, 
integrating factors.
Converting systems of first order DEs to higher order DEs and vice versa.
Second order linear IVPs
Wronskian -what it is, what being zero or nonzero means. How to compute it
  w/o solving DE.
reduction of order (given one solution find the other)
variation of parameters (to solve nonhomogeneous linear 1st and 2nd order IVPs)
classification of singular points of 2nd order linear IVPs (ordinary points,
 regular singular points, irregular singular points).
Series solution at ordinary points. 
Fuchs theorem. How many linearly indep solutions, and their radii of
 guaranteed convergence.
Solution(s) of Frobenius form at regular singular points.
Indicial equation.
What is solution if roots of indicial equation differ by an integer?
 (by limit of unequal case or by memory)
Dirac delta `function' -know properties and simple manipulations.
Green's functions -relation of solution to Ly=delta(t-tau) to the
  general nonhomogenous solution Ly=f(t) (for IVP and BVP).
Laplace transforms and their general properties. Transforms of derivatives.
Solving 2nd order linear ODEs and delay-differential eqs by Laplace transform.
Inversion of LT by table and shift etc theorems.
Inversion of LT by Mellin formula and the Bromwich contour.
Simple boundary value problems (at level of PS4).

What isn't examinable (incomplete list!):
Details of proofs of theorems.
Details of examples given in class or on homeworks (e.g.
 Jacobians of spherical coordinates, Chebyshev functions,
 delay differential equation for cruise control...)