Chapter 14 Multiple choice questions

* not completed

. If (∂F/∂x)_yz = 2xy + z²/x, what can be deduced about F(x,y,z) ?

F = xy² + z³/(3x) + g(x) correct incorrect

F = 2y - z²/x² + g(y,z) correct incorrect

F = x²y + z² ln(x) + g(y,z) correct incorrect

F = 2x + 2z/x + g(x) correct incorrect

* not completed

. Given that dF = [x^-1 - (y/x)²] dx + 2(y/x) dy, what is F(x,y) ?

F = ln(x) + (y/x)³/3 + k correct incorrect

F = - x^-2 + 2y/x + k correct incorrect

F = - x^-2 + (y/x)² + k correct incorrect

F = ln(x) + y²/x + k correct incorrect

* not completed

. Which of the following partial differential equations represents a diffusive process for the quantity Ω, where x and y are spatial coordinates and t is time?

∂²Ω/∂x² = K ∂Ω/∂t, K>0 correct incorrect

c² ∂²Ω/∂x² = ∂²Ω/∂t² correct incorrect

∂²Ω/∂x² + ∂²Ω/∂y² = 0 correct incorrect

∂²Ω/∂x² + ∂²Ω/∂y² = f(x,y) correct incorrect

* not completed

. Which of the following functions y(x,t), where 0=x=L and t=0, are separable solutions of the one-dimensional wave equation that satisfy the boundary conditions y(0,t)=0, ∂y/∂x(L,t)=0 and ?y/∂t(x,0)=0 ?

sin(kx) sin(kct) with k=nπ/L where n=1,2,3,… correct incorrect

sin(kx) cos(kct) with k=(2n+1)π/(2L) where n=0,1,2,3,… correct incorrect

cos(kx) sin(kct) with k=nπ/L where n=1,2,3,… correct incorrect

cos(kx) cos(kct) with k=(2n+1)π/(2L) where n=0,1,2,3,… correct incorrect

* not completed

. Which of the following is not true about the method of separation of variables for solving partial differential equations.

It reduces the problem into an equivalent set of ordinary differential equations. correct incorrect

For (homogeneous) linear equations, the general solution is a sum of separable solutions. correct incorrect

Commonly met equations can always be solved in this way. correct incorrect

It's simply a trial solution, with no a priori guarantee that the method will be successful. correct incorrect