1.
What does an Eigenvalue actually mean? Finish this sentence:An Eigenvalue, when subtracted from the diagonals of a matrix,:
A.
Causes the matrix to be linearly dependent.
B.
Causes the inverse to be impossible to solve.
C.
Causes the determinant to be 0.
D.
All of these statements are correct.
2.
What is the determinant of the B matrix?
A.
B.
C.
D.
None of these are correct.
3.
For the matrix shown, compute the eigenvalues and choose them from the list below.
A.
B.
C.
D.
E.
None of these are correct.
4.
For the matrix shown, compute the eigenvectors and choose them from the list below.(Choose the most correct answers, you may choose more than one).
A.
B.
C.
D.
E.
All of these are correct.
5.
Consider this mass-spring-damper system. Which of the following matrices is a correct description of this system?
6.
Consider the Taylor series T(x+a) = T(x) + a*dT/dx + ________ . What is the next term of this series?
7.
Consider the Taylor series T(x-a) = T(x) - a*dT/dx + _______. What is the next term of this series?
8.
Attached here is a code to compute the new temperature T_new using the FTCS method. This is a 1D problem with N cells. Someone believes there are some bugs in this code. Which lines are these bugs on?
A.
There are no bugs in this code.
B.
C.
D.
E.
9.
Consider the 1D bar shown in this figure. The temperature at the left end is fixed (T = 1). The temperature at the right end is fixed (T = 0). If the temperatures T1 to T5 are initially 1, what is the temperature at T3 if we wait until the solution is steady?
A.
B.
C.
D.
I don't have enough information.
10.
Consider the 1D bar shown in this figure. The temperature at the left end is fixed (T = 1). The temperature at the right end is fixed (T = 0). If the temperatures T1 to T5 are initially 0, the thermal diffusivity is 0.5, what is the temperature at T1 after one time step if dt = 0.15?
A.
B.
C.
D.
None of these options are correct.
11.
Consider the function shown f(x). For the fourier series shown, what is the value of a0?
12.
Consider the function shown f(x). For the fourier series shown, what is the value of an?
A.
B.
C.
D.
None of these options are correct.
13.
Consider the function f(x) shown here. What is the value of bn?
A.
B.
C.
D.
None of these options are correct.
14.
Choose an option below to complete the following sentence: A "periodic function" is a function which:
A.
B.
Satisfies the expression f(t+T) = f(t)
C.
Satisfies the expression f(t+T) = -f(t)
D.
15.
Consider the periodic function shown. What is the value of a0 for this function?
A.
B.
C.
D.
None of these solutions are correct.
16.
For the function shown here, what is the value of a0 for its Fourier series?
A.
B.
C.
None of these options are correct.
D.
17.
Two bars of some material with length 0.5 initially have temperatures T1 = 5 (left bar) and T2 = 1 (right bar). The thermal diffusivity of the material is 1, and the ends are insulated. Which of the following correctly describes the transient solution?
18.
For the 1D Wave Equation, we may use the method of separation of variables by assuming u(x,t) = A(x)B(t). Using this method, which of the following options is correct for the wave equation?
A.
A'' + kA = 0 (k = constant)
B.
B' - CkB = 0 (C, k = constant)
C.
B'' + CkB = 0 (C, k = constants)
D.
A'' - kA = 0 (k = constant)
19.
Consider the Fourier series shown here. When L = 1, this Fourier series with 3 terms equals f(0.4) = [Blank]. (Fill in the blank space). Use two decimal points - i.e. if your answer = 12.469, type 12.46 in the blank spot. Do not round up or down.