ECH 259 F2015, HW#5
Due Thu Nov 5, 10AM, smartsite
These questions constitute a practice exam for the midterm. The content will be
similar, but the complexity will be lower to accommodate a reasonable exam period.
Q1. Solve using eigenfunction expansions

ECH 259 F2015, HW#4
Due Tue Oct 27, 10AM, smartsite
Re: the size of Fourier coecients, Eq. (30) on p 29 of the class notes.
In question 1, we will derive a broadly similar result for any series based on SturmLiouville eigenfunctions, and use this result t

ECH 259 F2015, HW#3
Due Thu Oct 15, 10AM, smartsite
1. Re:
d2 y
= 2 y.
dx2
(1)
For each domain and boundary condition, determine the eigenfunctions, the eignevalues , and evaluate the normalization integral
b
y2 dx.
a
i) Domain: [0, L], homogeneous Dirich

ECH 259 F2015, HW#1
Due Thu Oct 1, 10AM, smartsite
Re: the linear second-order ODE
y + P(x)y + Q(x)y = R(x).
Let y1 and y2 be solutions to the homogeneous ODE (i.e., R(x) = 0). These two
solutions are independent if the Wronskian is nonzero:
W(x) = y1 y2

ECH 259 F2015, HW#1
Due Thu Oct 8, 10AM, smartsite
The equation
1
y
m2
sin
y = y,
sin
sin2
with m 0 an integer, will be important when solving certain PDEs in spherical coordinates.
(1) With x = cos , change variables from to x and write the dierentia