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 I made a graph in Excel which graphs (1/x^2) vs (1/cos^2 (angle of incidence)). From the graph I am supposed to analyze the slope and intercept of the straight line. I made a trendline which came out to be y=mx + b = (-0.0084)x + 5.54. From this equation I'm supposed to...

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...