Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 11.3, Problem 7E
To determine
Whether the function
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Discuss and explain in the picture
Consider the cones
K =
= {(x1, x2, x3) | € R³ :
X3
≥√√√2x² + 3x²
M =
= {(21,22,23)
(x1, x2, x3) Є R³: x3 >
+
2
3
Prove that M = K*.
Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the
formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where
AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix
A.
I am unable to solve part b.
Chapter 11 Solutions
Differential Equations with Boundary-Value Problems
Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...
Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 13 and 14 verify by direct integration...Ch. 11.1 - In Problems 13 and 14 verify by direct integration...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - From Problem 1 we know that f1(x) = x and f2(x) =...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - Prob. 21ECh. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Relate the orthogonal set B in Problem 27 with a...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 1–16 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - Prob. 13ECh. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 17 and 18 sketch the periodic...Ch. 11.2 - In Problems 17 and 18 sketch the periodic...Ch. 11.2 - Use the result of Problem 5 to show that...Ch. 11.2 - Prob. 20ECh. 11.2 - Use the result of Problem 7 to show that...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - Prob. 2ECh. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - Prob. 15ECh. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - Prob. 17ECh. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - In Problems 1-10 determine whether the function is...Ch. 11.3 - In Problems 1-10 determine whether the function is...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - Prob. 24ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 34ECh. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - Prob. 37ECh. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - Prob. 39ECh. 11.3 - In Problems 3942 suppose the function y = f(x), 0 ...Ch. 11.3 - In Problems 3942 suppose the function y = f(x), 0 ...Ch. 11.3 - Prob. 42ECh. 11.3 - In Problems 43 and 44 proceed as in Example 4 to...Ch. 11.3 - In Problems 43 and 44 proceed as in Example 4 to...Ch. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Suppose a uniform beam of length L is simply...Ch. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.4 - Consider y + y = 0 subject to y(0) = 0, y(L) = 0....Ch. 11.4 - Consider y + y = 0 subject to the periodic...Ch. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - (a) Find the eigenvalues and eigenfunctions of the...Ch. 11.4 - (a) Find the eigenvalues and eigenfunctions of the...Ch. 11.4 - Laguerres differential equation xy + (1 x)y + ny...Ch. 11.4 - Hermites differential equation y2xy+2ny=0,n=0,1,2,...Ch. 11.4 - Consider the regular Sturm-Liouville problem:...Ch. 11.4 - (a) Find the eigenfunctions and the equation that...Ch. 11.4 - Prob. 13ECh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - In Problems 36 expand f(x) = 1, 0 x 2, in a...Ch. 11.5 - In Problems 36 expand f(x) = 1, 0 x 2, in a...Ch. 11.5 - In Problems 7-10 expand the given function in a...Ch. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - In Problems 15 and 16 write out the first five...Ch. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Prob. 24ECh. 11 - In Problems 16 fill in the blank or answer true or...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Consider the portion of the periodic function f...Ch. 11 - Prob. 19RECh. 11 - Find the eigenvalues and eigenfunctions of the...Ch. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RE
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