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Kreyszig - Advanced Engineering Mathematics 10e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 6 / 20

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
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1 2 3 4 5 6 7 8
0/3 0/3 3/3 –/5 1/1 –/1 2/2 –/2
Total
6/20 (30.0%)

  • Instructions

    Advanced Engineering Mathematics, 10th Edition by Edwin Kreyszig, published by John Wiley & Sons, is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self-contained subject matter parts for maximum flexibility. This edition provides instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines. The WebAssign component for this text includes links to the full eBook and instant student feedback on randomized online questions.

    Question 1 showcases grading for bases, which accepts any correct response. Try multiplying by a constant!

    Question 2 displays the format used for an answer that does not exist. Note the prompt used to instruct the student to enter DNE.

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    Question 4 demonstrates WebAssign's series grading.

    Question 5 uses differential equation grading. It will accept any general solution to the given ODE. Try different variable constants!

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    Question 7 demonstrates integral grading. The prompt reminds the student to use C for the constant of integration.

    Question 8 enforces answers in simplest form. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. 0/3 points  |  Previous Answers KreEngMath10 7.4.001. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 0/1 –/1
2/100 2/100 0/100
Total
0/3
 
Consider the given matrix, and complete the following. Hint: For the following questions, row-reduce the matrix and its transpose. (You may omit obvious factors from the vectors of these bases.)
16−122
−86−1
Find the rank.
Incorrect: Your answer is incorrect. seenKey

1
Find a basis for the row space.

Incorrect: Your answer is incorrect. seenKey

[8, -6, 1]
Find a basis for the column space.

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2. 0/3 points  |  Previous Answers KreEngMath10 7.4.034. My Notes
Question Part
Points
Submissions Used
1 2 3
0/1 –/1 –/1
1/100 0/100 0/100
Total
0/3
 
Is the given set of vectors a vector space?
(v1, v2,   
 denote components.)
All vectors in Rn with
|vj| = 9
 for
j = 1,   , n
     Incorrect: Your answer is incorrect.
Determine the dimension. (If the answer does not exist, enter DNE.)
Find a basis. (Enter each vector as a comma-separated list of its components. Enter numerical values only. Include parentheses around each vector, and separate vectors with a comma. If the answer does not exist, enter DNE.)

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3. 3/3 points  |  Previous Answers KreEngMath10 10.5.005. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
Total
3/3
 
Consider the following surface.
Paraboloid of revolution
r(u, v) = [u cos(v), u sin(v), u2]
Familiarize yourself with parametric representations of important surfaces by completing the following.
What is a representation
z = f(x, y)
  or  
g(x, y, z) = 0
 of the surface?
z =
x2+y2
Correct: Your answer is correct. webMathematica generated answer key
Find the parameter curves (curves
u = const
 and
v = const)
 of the surface.
     Correct: Your answer is correct.
Find a normal vector
N = ru ✕ rv
 of the surface. (Enter each vector as a comma-separated list of its components. Include parentheses around your answer.)
(x, y, z) =
(−2ش2جس(ا)​,−2ش2سن(ا)،ش)

Your answer includes 11 characters that can't be graded.

Delete your recent changes and use the pad tools to finish your answer. More information

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4. –/5 points KreEngMath10 11.1.012. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
Find the Fourier series of the given function
f(x),
 which is assumed to have the period 2π. Show the details of your work.
f(x) = |x|
f(x) =
+ 
∞
n = 1
Sketch or graph the partial sums up to that including
cos(5x)
 and
sin(5x).
n = 1

n = 3

n = 5

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5. 1/1 points  |  Previous Answers KreEngMath10 12.1.019. My Notes
Question Part
Points
Submissions Used
1
1/1
1/100
Total
1/1
 
PDEs are solvable as ODEs if a PDE involves derivatives with respect to one variable only (or can be transformed to such a form), so that the other variable(s) can be treated as parameter(s). Solve the following for
u = u(x, y).
uy + y2u = 0
u =
ƒ(x)e{−(y33​)}
Correct: Your answer is correct. webMathematica generated answer key

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6. –/1 points KreEngMath10 12.4.019. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Longitudinal vibrations of an elastic bar or rod in the direction of the x-axis are modeled by the wave equation
utt = c2uxx, c2 = E/ρ.
† If the rod is fastened at one end,
x = 0,
 and free at the other,
x = L,
 we have
u(0, t) = 0
 and
ux(L, t) = 0.
 The motion corresponding to initial displacement
u(x, 0) = f(x)
 and initial velocity is as follows.
u = 
∞
n = 0
An sin(pnx) cos(pnct),
An = 
2
L
L
0
f(x) sin(pnx) dx
Find
pn
 where
n = 1, 2, 3...
pn =

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7. 2/2 points  |  Previous Answers KreEngMath10 13.4.013. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 3/100
Total
2/2
 
Is the following function harmonic?
u = xy
     Correct: Your answer is correct.
If your answer is yes, find a corresponding analytic function
f(z) = u(x, y) + iv(x, y).
 (Use C for the constant of integration. If your answer is no, enter NONE.)
f(z) =
i(−12​z2+C)
Correct: Your answer is correct. webMathematica generated answer key

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8. –/2 points KreEngMath10 13.6.003. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Find the following. (Enter your answers in terms of z. Simplify your answers completely.)
cosh2(z) − sinh2(z),
  
cosh2(z) + sinh2(z)
cosh2(z) − sinh2(z) =
cosh2(z) + sinh2(z) =

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