Deck 12: Boundary-Value Problems in Rectangular Coordinates

Question 1

The general solution of is

A)
B)
C)
D)
E)

Answer 1

B

Question 2

The solution of the eigenvalue problem from the previous problem is

A)
B)
C)
D)
E)

Answer 2

E

Question 3

The wave equation for a vibrating string is derived using the assumptions Select all that apply.

A) the string is perfectly flexible.
B) the displacements may be large.
C) the tension acts perpendicular to the string.
D) the tension is large compared with gravity.
E) the string is homogeneous.

Answer 3

A, D, E

Question 4

The differential equation is

A) first order, linear, homogeneous
B) first order, linear, non-homogeneous
C) second order, nonlinear
D) second order, linear, homogeneous
E) second order, linear, non-homogeneous

Question 5

The differential equation is Select all that apply.

A) nonlinear
B) linear
C) hyperbolic
D) elliptic
E) parabolic

Question 6

In the previous three problems, the solution of the original problem is

A) , where
B) , where
C) , where
D) , where
E) , where

Question 7

The solution of the eigenvalue problem from the previous problem is

A)
B)
C)
D)
E)

Question 8

In the previous three problems, the solution of the original problem is

A) , where
B) , where
C) , where
D) , where
E) , where

Question 9

The differential equation is Select all that apply.

A) linear
B) nonlinear
C) hyperbolic
D) elliptic
E) parabolic

Question 10

Consider the equation with conditions . When separating variables with , the resulting problems for are

A)
B)
C)
D)
E)

Question 11

Consider the equation with conditions . When separating variables with , the resulting problems for are

A)
B)
C)
D)
E)

Question 12

In the previous two problems, the product solutions are

A)
B)
C)
D)
E)

Question 13

The solution of the previous three problems is , where and are given in the previous problem and

A)
B)
C)
D)
E)

Question 14

After separating variables in the previous problem, the eigenvalue problem becomes

A)
B)
C)
D)
E)

Question 15

In the previous two problems, the product solutions are

A)
B)
C)
D)
E)

Question 16

The solution of is

A)
B)
C)
D)
E)

Question 17

When is substituted into the equation , the resulting equations for and are

A)
B)
C)
D)
E)

Question 18

The solution of the eigenvalue problem in the previous problem is

A)
B)
C)
D)
E)

Question 19

The solution of if is

A)
B)
C)
D)
E)

Question 20

The model describing the temperature in a rod where the temperature at the left end is zero and where there is heat transfer from the right boundary into the external medium is

A)
B)
C)
D)
E)

Question 21

Consider the equation with conditions . When separating variables with , the resulting problems for are

A)
B)
C)
D)
E)

Question 22

In the previous problem, the eigenfunction expansion if is

A)
B)
C)
D)
E)

Question 23

When is substituted into the equation , the resulting equations for and are

A)
B)
C)
D)
E)

Question 24

The solution of the eigenvalue problem from the previous problem is

A)
B)
C)
D)
E)

Question 25

The solution of the eigenvalue problem from the previous problem is

A)
B)
C)
D)
E)

Question 26

The solution of is

A)
B)
C)
D)
E)

Question 27

The differential equation is Select all that apply.

A) linear
B) nonlinear
C) hyperbolic
D) elliptic
E) parabolic

Question 28

In the previous three problems, the solution of the original problem is

A) , where
B) , where
C) , where
D) , where
E) , where

Question 29

In the previous two problems, the product solutions are

A)
B)
C)
D)
E)

Question 30

The differential equation is

A) first order, linear, homogeneous
B) first order, linear, non-homogeneous
C) second order, nonlinear
D) second order, linear, homogeneous
E) second order, linear, non-homogeneous

Question 31

In the problem , the eigenvalues and eigenfunctions of the underlying homogeneous problem are

A)
B)
C)
D)
E)

Question 32

The quantity of heat in an element of a rod of mass is proportional to Select all that apply.

A) mass
B) thermal conductivity
C) specific heat
D) thermal diffusivity
E) temperature

Question 33

In the previous two problems, the solution for takes the form

A)
B)
C)
D)
E)

Question 34

In the previous two problems, the product solutions are

A)
B)
C)
D)
E)

Question 35

Consider the equation with conditions . When separating variables with , the resulting problems for are

A)
B)
C)
D)
E)

Question 36

In the previous three problems, the solution of the original problem is

A) , where
B) , where
C) , where
D) , where
E) , where

Question 37

The general solution of is

A)
B)
C)
D)
E)

Question 38

The solution of if is

A)
B)
C)
D)
E)

Question 39

In the previous three problems, the solution for is

A)
B)
C)
D)
E)

Question 40

The differential equation is Select all that apply.

A) linear
B) nonlinear
C) hyperbolic
D) elliptic
E) parabolic