Physics 498/MMA
Handout MT
Oct 29th 2003
Mathematical Methods in Physics I
http://w3.physics.uiuc.edu/
∼
mstone5
Prof. M. Stone
2117 ESB
University of Illinois
Do question
one
, and then any
two
of the other three questions.
Try to answer entire
questions. Little, if any, credit will be given for fragmentary answers.
1) Green Function
: Consider the
homogeneous
boundary value problem

y
00
=
f
(
x
)
,
y
(0) =
y
0
(1) = 0
.
a) Construct the explicit Green function appropriate to this problem. (5 points)
b) Use your Green function to write down the solution of the boundary value problem as
the sum of two explicit integrals over complementary components of the unit interval.
(5 points)
c) ConFrm that your solution
y
(
x
) obeys both boundary conditions, and that it does
indeed solve the original problem. (5 points)
Now consider the
inhomogeneous
boundary value problem

y
00
=
f
(
x
)
,
y
(0) =
A,
y
0
(1) =
B.
d) Use the method based Lagrange’s identity to obtain the solution to this boundary value
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 Fall '07
 Stone
 Derivative, Boundary value problem

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