Recent content by kgal

Homework Statement Hey guys, I have this problem which I am having a hard time solving. $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$ $$u(x,0)=0$$ $$u_t(x,0)=g(x)$$ $$u(1,t)=0=u(2,t)$$ Homework Equations $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$...

Homework Statement I have 3 equations: \frac{\partial^2 u}{\partial t^2}+\frac{\partial^2 u}{\partial x \partial t}+\frac{\partial^2 u}{\partial x^2} \frac{\partial^2 u}{\partial t^2}+4\frac{\partial^2 u}{\partial x \partial t}+4\frac{\partial^2 u}{\partial x^2} \frac{\partial^2...

Great! I got it! How would I solve this problem using a technique like changing variables instead of separation of variables?

So you're saying that I need to set u(x,t)= u_tt-u_xx = f(t)sin(∏x)? How do I find the function f(t)? What I did was this: found u_xx, u_tt and plugged them into u_tt - u_xx = sin(∏x). What do I do with the boundary conditions and the initial conditions (how do they factor in)?

Homework Statement If utt - uxx= 1-x for 0<x<1, t>0 u(x,0) = x2(1-x) for 0≤x≤1 ut(x,)=0 for 0≤x≤1 ux(x,)=0 u(1,t)=0 find u(1/4,2) Homework Equations The Attempt at a Solution I was thinking to make a judicious change of variables that not only converts the PDE to a homogenous PDE, but also...

So basically something like Autt-Bxx= sin∏x and Cutt-Duxx=0 and then sum the up into a solution u(x,t)?

Homework Statement Find the solution of: utt-uxx = sin(∏x) for 0<x<1 u(x,0)=0 for 0<=x<=1 ut(x,0)=0 for 0<=x<=1 u(0,t)=0 u(1,t)=0Homework Equations utt-uxx = sin(∏x) for 0<x<1 u(x,0)=0 for 0≤x≤1...

Homework Statement Let f and g be sufficiently smooth real-valued (scalar-valued) functions and let u be a sufficiently smooth vector-valued function on a region V of (x1; x2; x3)-space with a sufficiently smooth boundary ∂V . The Laplacian
Δf of f: Δf:=∇*∇f=∂2f/∂x21 + ∂2u/∂x22 +...

Homework Statement A wave of wavelength 75 cm has velocity 375 m/s. a. What is the spatial separation between two points that are 30° out of phase at a particular time? b. What is the phase change at a particular position for a time change of 0.5 ms? Homework Equations u = λ / T...

Homework Statement A square loop, with sides of length L, carries current i. Find the magnitude of the magnetic field from the loop at the center of the loop, as a function of i and L. Homework Equations B=μ0/4∏∫i * dl X r^ /r^2 The Attempt at a Solution

Homework Statement Suppose that the magnetic field of the Earth were due to a single current moving in a circle of radius 1758 km through the Earth's molten core. The strength of the Earth's magnetic field on the surface near a magnetic pole is about 6. 10^-5 T. About how large a current would...

in the specific case of this problem they come out like this: ∂z/∂r = (∂z/∂x)(∂x/∂r) + (∂z/∂y)(∂y/∂r) ∂z/∂θ = (∂z/∂x)(∂x/∂θ ) + (∂z/∂y)(∂y/∂θ) right?

Homework Statement let z=f(x,y) be a differentiable function. If we change to polar coordinates, we make the substitution x=rcos(θ), y=rsin(θ), x^2+y^2=r^2 and tan(θ) = y/x. a. Find expressions ∂z/∂r and ∂z/∂θ involving ∂z/∂x and ∂z/∂y. b. Show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 +...

Homework Statement 6. Three disease-carrying organisms decay exponentially in seawater according to the following model: P(t) = Ae-1.5t + Be-0.3t + Ce-0.05t t 0.5, 1, 2, 3 , 4, 5, 6, 7, 9 p(t) 6, 4.4, 3.2, 2.7, 2, 1.9, 1.7, 1.4, 1.1 Estimate the initial concentration of each...

Homework Statement A potential difference of 160V is applied across two col-linear conducting cylinders. the radius of the outer cylinder is 15 cm, the radius of the inner cylinder is 10 cm, the height of the two cylinders is 38 cm. a. How much charge is applied to each of the cylinders? b...