Homework Statement
http://img51.imageshack.us/img51/853/39983853.jpg
2. The attempt at a solution
Q3.1
I get the general solution as
x(t) = Ae^{3t}+Be^{-t} + cost - 2sint .
Q3.2
Letting
y=\dot{x}
and using the general solution, we get...
Homework Statement
Quite a long intro to the question so I thought it easier to include it as an image:
http://img96.imageshack.us/img96/7264/78941753.jpg
http://img686.imageshack.us/img686/7780/39557949.jpg
The Attempt at a Solution
I can do Q2.3 and get the payoff matrix...
Homework Statement
Quite a long intro to the question so I thought it easier to include it as an image:
http://img96.imageshack.us/img96/7264/78941753.jpg
http://img686.imageshack.us/img686/7780/39557949.jpg The Attempt at a Solution
I can do Q2.3 and get the payoff matrix given when V=4...
Homework Statement
Consider
f(x)=\sum\frac{1}{n(1+nx^{2})}
from n=1 to n=infinity.
On what intervals of the form (a,b) does the series converge uniformly? On what intervals of the form (a,b) does the series fail to converge uniformly?
Homework Equations
Weierstrass M-test...
Homework Statement
Calculate the outward flux of the two dimensional vector field
f:\Re^{2}\rightarrow\Re^{2} , f(x,y)=(x/2 + y\sqrt{x^{2}+y^{2}},y/2 + x\sqrt{x^{2}+y^{2}})
through the boundary of the ball
\Omega = {(x,y)\in\Re^{2} \left| x^{2}+y^{2} \leq R^{2}} \subset\Re^{2}, R>0...
Yeah I get a similar thing. So we get a turning point of Q at some value t=-psi/phi, and when you put this back into Q you get
\int0 = constant.
Am I being really dumb cos I can't seem to get anything like the inequality from this :((((
Cheers.
Homework Statement
Let
\phi,\psi : [a,b] \rightarrow \Re
be step functions.
Prove that
(\int \phi\psi)^{2} \leq (\int\phi^{2})(\int\psi^{2}) .
Hint: Consider the quadratic function of a real variable t defined by
Q(t)=\int(t\phi+\psi)^2 .
The Attempt at a Solution...
Homework Statement
Let \underline{r} be a regular parameterisation of a space curve C \subset R^{3}. Prove that
\kappa=\frac{\left\|\underline{\dot{r}}\times\underline{\ddot{r}}\right\|}{\left\|\underline{\dot{r}}\right\|^{3}} .
The Attempt at a Solution
We have...
I'm just learning a bit about the "minimal polynomial" today but there was a section from the book which I didn't understand. This is the section, and I've circled the bit I'm having trouble with.
http://img15.imageshack.us/img15/1825/97503873.jpg (sorry, it won't let me post an image for...
Homework Statement
http://img195.imageshack.us/img195/4873/46343978.jpg
The Attempt at a Solution
Part (a) is simple enough, i get
\dot{x}=y
\dot{y}=x^{3}-x.
Equilibrium points occur when the time-derivatives of both x and y are zero, which gives the 3 equilibrium points...
Homework Statement
http://img30.imageshack.us/img30/9954/72990922.jpg
The Attempt at a Solution
I would say the answer to (a) was no but that would be a guess. Does it have to do with the fact that it's done instantaneously, whereas to achieve anything like an irreversible process...