5311 Spr 2011
Take home midterm solution
Problem #3, parts (b)-(e)
Write a function to evaluate the Rayleigh quotient
Qu
In[5]:=
:
Integrate x D u, x ^ 2, x, 0, 1
Integrate x u ^ 2, x, 0, 1
Compute Q
Math 5311 Spr 2011 - Midterm take-home exam solutions
Problem #1
Part (a)
N
Assume an approximate solution u ( x, t) = n=1 an (t) n ( x ) . The spatial basis functions n ( x ) are chosen so
that they
Math 5311 Midterm review
1. Inhomogeneous BCs
(a) Shifting data
2. Greens functions
(a) Denitions and basic properties:
i. given a BVP you want to solve, nd a BVP that denes the Greens function.
ii. G
Math 5311 Spr 2011 - Midterm exam solutions
1. Solving the BVP
d
du
(x)
= f1 (x)
dx
dx
u (0) = 0
u (1) = 0
by Greens functions.
(a) To obtain the Greens function G ( x, x ) you would need to solve th
Math 5311 Spr 2011 - Homework #1 Solutions
Problem 1
Part (a)
dv W =
d
=
dt
d
W (u + tv)|t=0
dt
1
e(u+vt) d x
1
1
t =0
e(u+vt) v d x
=
1
t =0
1
e(u ) v d x
=
1
Part (b)
d
dv W =
dt
1
u +v t
2
+ (u + v