Let denote the L2 inner product on the interval 0, Suppose u(x) satisfies u(0) u(t) 0 Write out the integration by parts formula ( Icirc acute y, u) ( Iuml y, u) ( Iuml y,u ') and then justify it by direct analysis of the resulting integrals lf,g) f(x) g(x) dx...

Let denote the L2 inner product on the interval [0, ]. Suppose u(x) satisfies u(0) = u(t)

Question:

Let

denote the L2 inner product on the interval [0, „“]. Suppose u(x) satisfies u(0) = u(t) = 0. Write out the integration by parts formula (Î´y, u) = (Ïƒy, u) = - (Ïƒy,u'). and then justify it by direct analysis of the resulting integrals.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 18, 2016 09:04 AM

See More Questions

Verify the Cauchy-Schwarz inequality for the functions f(x) = x and g(x) = e' with respect to (a) the L2 inner product on the interval [0, 1 ], (b) the L2 inner product on [ - 1, 1 ], (c) the...
Using the L2 inner product on the interval [0, nr] find the angle between the functions (a) 1 and cos x (b) 1 and sin x (c) cos x and sin x
(a) Show that the polynomials p1(x) = 1, p2(x) - 1/2 - p3(x) = x2 - x + 1/6 are mutually orthogonal with respect to the L2 inner product on the interval [0, 1 ]. (b) Show that the functions sin n x,...
The bank portion of the bank reconciliation for Katsaris Company at August 31, 2014, was as follows: The adjusted cash balance per bank agreed with the cash balance per books at August 31. The...
1. These examples show people at different stages of their professional lives choosing to become business owners with the help of a franchise. What conclusions can you draw from their stories about...
Can you name products and services that, in your opinion, have relatively poor quality? Relatively high quality? Are companies that provide high-quality products more successful? How can you tell?
A sphere of \(30-\mathrm{mm}\) diameter contains an embedded electrical heater. Calculate the power required to maintain the surface temperature at \(89^{\circ} \mathrm{C}\) when the sphere is...
Due to rapid turnover in the accounting department, a number of transactions involving intangible assets were improperly recorded by Wasp Company in 2010. 1. Wasp developed a new manufacturing...
Assessment in the Transition Process. Objective: To explore, examine and discover the process and types of assessments supporting transition programs and services. a. click on this link to review...
1. What approaches would you recommend the Blue Ocean Strategy team use to identify new market space for the conglomerate? 2. How realistic is it for Baxter to delegate the task of finding a Blue...
Let y a. b. s(x) = %3D zp (2)'g
Let (k)lx) denote the kth derivative of the delta function <5v(x). Justify the formula (8(yk\u) = (-1 )k u(k\y) whenever u is k times continuously differentiable.
Find the x- and y-intercepts. Then graph each equation. 2 3 x - 3y = 7
The open-loop transfer function of a feedback control system is \[ \mathrm{G}(s) \mathrm{H}(s)=\frac{1}{(s+1)^{3}} \] The gain margin of the system is (a) 2 (b) 4 (c) 8 (d) 16
A system has fourteen poles and two zeros. The slope of its highest frequency asymptote in its magnitude plot is (a) - \(40 \mathrm{~dB} /\) decade (b) - \(240 \mathrm{~dB} /\) decade (c) \(-280...
The magnitude frequency response of a control system is shown below. The value of \(\omega_{1}\) and \(\omega_{2}\) are respectively (a) 10 and 200 (b) 20 and 200 (c) 20 and 400 (d) 100 and 400 gain...
The transfer function of a closed-loop system is \[ \mathrm{T}(s)=\frac{\mathrm{K}}{s^{2}+(3-\mathrm{K}) s+1} \] where \(\mathrm{K}\) is the forward path gain. The root locus plot of the system is...
The amplitude ratio \(A(\omega)\) and phase shift function \(\phi(\omega)\) for irrational transfer function \(\mathrm{G}(s)=\frac{e^{-4 s}}{s}\) respectively are (a) \(\mathrm{A}(\omega)=-4 \omega,...
An annual report of Marriott International, Inc., contained a rather lengthy narrative entitled Liquidity and Capital Resources. The narrative noted that a revolving credit agreement outstanding at...
Show that if A is any m n matrix, then Im A = A and AIn = A.
There exists a function f such that f(x) < 0, f(x) < 0, and f(x) > 0 for all x.
If f and g are increasing on an interval l, then f + g is increasing on l.
If f and g are increasing on an interval l, then f g is increasing on l.
What extent does emotional intelligence among leaders and employees contribute to effective teamwork and conflict resolution, and what methods can be employed to enhance emotional intelligence within...
Determine the exponential function y = c(b) that goes through the points (-2, 16) and (1,54). Algebraic work must be shown for full credit.
Solve 6. 8. 8 So log x (1 + x)(4+ x) [log x] 2 dx 0 1 + x So dx

Let denote the L2 inner product on the interval [0, ]. Suppose u(x) satisfies u(0) = u(t)

Question:

lf,g)=| f(x) g(x) dx

Step by Step Answer:

y u while ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions