Consider the equation uux + uy = 0 with the initial
condition
u(x, 0) = h(x) = ⇢ 0 for x > 0
uo for x < 0, with
uo< 0.
Show that there is a second weak solution with a shock along the
line x = uo y / 2
The solution in both mathematical and graphical presentation
before and after the shock.
1. Calculate the Transversality Conditions
2. and then solve the ff:
a.) Ux +Uy =1-U
U (X, X+X^2) = SIN X
b) XUx + YUy= 4U
with initial condition u=1 on the unit circle x^2 +y^2 =1
( you will need to parameterize the circle in terms of parameter
r).
Consider a semi-infinite square well: U(x)=0 for 0 ≤ x ≤ L,
U(x)=U0 for x > L, and U(x) is infinity otherwise.
Determine the wavefunction for E < Uo , as far as possible,
and
obtain the transcendental equation for the allowable energies E.
Find the necessary condition(s) on E for the solution to exist.
utility function u(x,y;t )= (x-t)ay1-a
x>=t, t>0, 0<a<1
u(x,y;t )=0 when x<t
does income consumption curve is
y=[(1-a)(x-t)px]/apy ?(my result, i used
lagrange, not sure about it)
how to draw the income consumption curve?