Deck 14: Integral Transform Method

Question 1

The solution of the integral equation is

A)
B)
C)
D)
E) none of the above

Answer 1

B

Question 2

In the three previous problems, the solution for is

A)
B)
C)
D)
E)

Answer 2

B

Question 3

Let . The Fourier integral representation of f is

A)
B)
C)
D)
E) none of the above

Answer 3

C

Question 4

In the previous problem, the solution for is

A)
B)
C)
D)
E)

Question 5

In the previous problem, the integral converges at to the value

A) 0
B)
C) 1
D) 2
E)

Question 6

The value of is

A)
B)
C)
D)
E) none of the above

Question 7

The value of is

A)
B)
C)
D)
E) none of the above

Question 8

In the previous two problems, the integral converges for to the function

A)
B)
C)
D) 1
E) none of the above

Question 9

In the previous three problems, the solution for is

A)
B)
C)
D)
E)

Question 10

The complementary error function is defined as

A)
B)
C)
D)
E)

Question 11

In the previous problem, assume that . The solution for is

A)
B)
C)
D)
E)

Question 12

Apply a Fourier transform in in the previous problem. The resulting equation for is

A)
B)
C)
D)
E)

Question 13

The Fourier cosine integral of a function f defined on is

A)
B)
C)
D)
E)

Question 14

In the previous problem, the integral converges at to the value

A) 0
B) 1
C) 2
D) 3
E) 4

Question 15

In the previous problem, if is

A)
B)
C)
D)
E) 0

Question 16

Consider the temperature, , in an infinite rod , with an initial temperature of . The mathematical model for this is

A)
B)
C)
D)
E)

Question 17

In the previous problem, apply the Laplace transform. The resulting equation for is

A)
B)
C)
D)
E)

Question 18

Consider a semi-infinite, elastic, vibrating string, with zero initial position and velocity, driven by a vertical force at , so that . Assume that . The mathematical model for the deflection, , is

A)
B)
C)
D)
E)

Question 19

The value of is

A) 0
B) 1
C)
D)
E)

Question 20

The Fourier cosine integral of is

A)
B)
C)
D)
E)

Question 21

In the previous problem, assume that . The solution for is

A)
B)
C)
D)
E)

Question 22

The value of is

A)
B)
C)
D)
E) none of the above

Question 23

The error function is defined as

A)
B)
C)
D)
E)

Question 24

Consider the problem of finding the temperature in a semi-infinite rod with zero initial temperature and a fixed constant temperature, , at . The mathematical model for this problem is

A)
B)
C)
D)
E)

Question 25

The value of is

A)
B)
C)
D)
E)

Question 26

The value of is

A) 0
B) 1
C)
D)
E)

Question 27

The Laplace transform of a function f is

A)
B)
C)
D)
E)

Question 28

The Fourier integral representation of a function f is given by

A)
B)
C)
D)
E)

Question 29

In the three previous problems, the solution for the temperature is

A)
B)
C)
D)
E)

Question 30

If is

A)
B)
C)
D)
E)

Question 31

In the previous problem, apply the Laplace transform. The resulting equation for is

A)
B)
C)
D)
E)

Question 32

Suppose . In the convolution theorem, the formula for the Fourier transform is Select all that apply.

A)
B)
C)
D)
E) none of the above

Question 33

The complex form of the Fourier integral of a function f is

A)
B)
C)
D)
E)

Question 34

In the previous problem, the integral representation converges at to the value

A) 0
B) 1
C)
D) -1
E) none of the above

Question 35

In the three previous problems, the solution for is

A)
B)
C)
D)
E)

Question 36

If is

A)
B)
C)
D)
E)

Question 37

Let . The Fourier integral representation of f is , where

A)
B)
C)
D)
E)

Question 38

Consider the problem of a vibrating string, tightly-stretched between and , with a fixed initial position, , and zero initial velocity. The mathematical problem for the deflection, , is

A)
B)
C)
D)
E)

Question 39

In the previous problem, apply a Fourier sine transform in x. The new problem for the transform is

A)
B)
C)
D)
E)

Question 40

In the previous problem, the solution is

A)
B)
C)
D)
E)