Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 14.4, Problem 18E
In Problems 1–21 and 24–26 use the Fourier integral transforms of this section to solve the given boundary-value problem. Make assumptions about boundedness where necessary.
In Problems 17 and 18 find the steady-state temperature u(x, y) in the plate given in the figure. [Hint: One way of proceeding is to express Problems 17 and 18 as two- and three-boundary-value problems, respectively. Use the superposition principle. See Section 12.5.]
18. 
FIGURE 14.4.2 Plate in Problem 18
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Chapter 14 Solutions
Differential Equations with Boundary-Value Problems
Ch. 14.1 - (a) Show that erf(t)=10ted. (b) Use part (a), the...Ch. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Use the third and fifth entries in Table 14.1.1 to...
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - A string is stretched along the x-axis between (0,...Ch. 14.2 - Prob. 2ECh. 14.2 - The displacement of a semi-infinite elastic string...Ch. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - The displacement u(x, t) of a string that is...Ch. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - In Problems 1118 use the Laplace transform to...Ch. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Show that a solution of the boundary-value problem...Ch. 14.2 - Prob. 21ECh. 14.2 - If there is a heat transfer from the lateral...Ch. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 16 find the Fourier integral...Ch. 14.3 - In Problems 1-6 find the Fourier integral...Ch. 14.3 - In Problems 712 represent the given function by an...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - In Problems 1316 find the cosine and sine integral...Ch. 14.3 - In Problems 17 and 18 solve the given integral...Ch. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.4 - In Problems 1-21 and 24-26 use the Fourier...Ch. 14.4 - Prob. 2ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 7ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - In Problems 121 and 2426 use the Fourier integral...Ch. 14.4 - Discussion problems 27. (a) Suppose...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - In Problems 1-20 solve the given boundary-value...Ch. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RE
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