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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 14 Multiple choice questions
Partial differential equations
Quiz Content
*
not completed
.
If (∂F/∂
x
)
_{yz}
= 2
xy
+
z
^{2}
/x, what can be deduced about F(
x
,
y
,
z
) ?
F =
xy
^{2}
+
z
^{3}
/(3
x
) + g(
x
)
correct
incorrect
F = 2
y

z
^{2}
/
x
^{2}
+ g(
y
,
z
)
correct
incorrect
F =
x
^{2}
y
+
z
^{2}
ln(
x
) + g(
y
,
z
)
correct
incorrect
F = 2
x
+ 2
z
/
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}
+ 2
y
/
x
+
k
correct
incorrect
F = 
x
^{2}
+ (
y
/
x
)
^{2}
+
k
correct
incorrect
F = ln(
x
) +
y
^{2}
/
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?
∂
^{2}
Ω/∂
x
^{2}
= K ∂Ω/∂t, K>0
correct
incorrect
c
^{2}
∂
^{2}
Ω/∂
x
^{2}
= ∂
^{2}
Ω/∂
t
^{2}
correct
incorrect
∂
^{2}
Ω/∂
x
^{2}
+ ∂
^{2}
Ω/∂
y
^{2}
= 0
correct
incorrect
∂
^{2}
Ω/∂
x
^{2}
+ ∂
^{2}
Ω/∂
y
^{2}
= 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 onedimensional wave equation that satisfy the boundary conditions y(0,
t
)=0, ∂y/∂
x
(L,
t
)=0 and ?y/∂
t
(
x
,0)=0 ?
sin(k
x
) sin(kc
t
) with k=nπ/L where n=1,2,3,…
correct
incorrect
sin(k
x
) cos(kc
t
) with k=(2n+1)π/(2L) where n=0,1,2,3,…
correct
incorrect
cos(k
x
) sin(kc
t
) with k=nπ/L where n=1,2,3,…
correct
incorrect
cos(k
x
) cos(kc
t
) 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
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