Homework Statement
Given the initial value problem:
\frac{(u)}{(1-e^-(2x))}u_{x}+ \frac{\sqrt{t}}{u}u_{t}=1, with x, t, u > 0
Subject to condition u(x,1)=e^{-x}
Homework Equations
a) Classify given partial differential equation.
b) Write the characteristic equations. By...
Homework Statement
The trajectory of an arrow in space obeys the following system of equations:
\dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2)
\dot{y} = y+(x^2+y^2-3)^2 (y^3-y+x^2y)
1. Questions
a) Derive an ODE for the radial coordiante r(t) = \sqrt[]{x^2(t)+y^2(t)}
b) Show that the...
Description
1. Prove that operators i(d/dx) and d^2/dx^2 are Hermitian.
2. Operators A and B are defined by:
A\psi(x)=\psi(x)+x
B\psi(x)=d\psi/dx+2\psi/dx(x)
Check if they are linear.
The attempt at a solution
I noted the proof of the momentum operator '-ih/dx'...
Homework Statement
Let S be a smooth surface enclosing the volume V, and let \vec{n} to be the unit outward normal. Using the Divergence Theorm show that:
∫∫ x \vec{r} ° \vec{n} dS = 4 * ∫∫∫ x dV,
where \vec{r}=(x,y,z)
Homework Equations
Divergence theorm...
Homework Statement
Hi. I think it will be easiest to understand if I upload a word document as it has some complicated characters. The bold letters stand for vectors.
http://www.sendspace.pl/file/1f830d4ff025d966f71b62c
Homework Equations
Divergence theorm...