Thank you in advance. This is PDE, Fourier series.
Thank you in advance. This is PDE, Fourier series. Define B: c[0,1]→ R by By =...
Please answer question number 2, Thank you
Engineering Mathematics (-) # 6 HM. olve the PDE of the vibrating string with given initial velocity and zero initial displacement by use of Fourier sine series. 02u(x,t) = c2-211(x,t) ax2 PDE. : t>0 0<x<L 2 , Ot , BCs u(0,1) 0u(L,t) 0, t20 IC u(x,0) = 0 , 0 x L : an(x,0) =h(x) 0 L x , ot in problem (1), u(x,t)=? (2). Suppose that h(x)-x(1-cos(-))
Engineering Mathematics (-) # 6...
Real Analysis: Define f: [0,1] -->
by f(x) = {0, x
[0,1] ; 1, x
[0,1]\
}
(a) Identify U(f) = inf{U(f, P): P
(a,b)}
(b) Prove or disprove that f is Darboux Integrable.
Thanks in advance!
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1. Define the function sgn by: ifx>0 ifx=0 sgn(x) = 0 Now define h(x): [0,1]R by 51 if0cz ifx=0 h(z) =(sgn(sin(1/4)) i Prove that h(x) is integrable.
Problem 4. Let 0<4 g(r) ecos (a) write the Fourier cosine series and the Fourier sine series respectively. (b) Draw the graph of the function g(r) and state which series is better and why.
Problem 4. Let 0
need the answer for G please and thank you
1. Find the Fourier series coefficients of the following periodic signals 2πη πη π x[n] = [1 + sin(一)I cos (C -) e. x[n] = ( 21)-) y[n-1], y[n] is a periodic signal with period N = 8 and Fourier f. series coefficients of bk - -bk -4 cOS
(b) Let a >0. Does (f.) converge uniformly on [-a, al? (c) Does (f) converge uniformly on R? Q4 You are given the series n2 +r2 (a) Prove that the series converges uniformly on [-a, al for each a > 0. (b) Prove that the sum F(r) is well defined and continuous on R. (c) Prove that the series does not converge uniformly on R. Q5 You are given the series I n2r2
(b) Let a >0. Does (f.) converge...
I need help with this one, thank you in advance
2. Consider the inner product space V = P2(R) with (5.9) = L 109(e) dt, and let T:V – V be the linear operator defined by T(S) = If'(x) + 2%(r) +1. (i) Compute T*(1+1+z?). (ii) Determine whether or not there is an orthonormal basis of eigenvectors B for which Tja is diagonal. If such a basis exists, find one.
3. Evaluating a Fourier series at a point: You may use any of the Fourier series we have de- rived in class, you have obtained in the homework or any in the Table of Fourier series in MyCourses (a) By evaluating a Fourier series at some point, show that 9 25 49 n (2n+1)2 Page 1 of 2 (b) Use another Fourier series different from the one used in class to show that 4 2n+1 (c) Use a Fourier series...
(4) Let(an}n=o be a sequence in C. Define R-i-lim suplanlì/n. Recall that R e [0,x] o0 is the radius of convergence of the power series Σ a (z 20)" Assume that R > 0 (a) Prove that if 0 < ρ < R, then the power series converges uniformly on the closed (b) Prove that the power series converges uniformly on any compact subset of the disk Ix - xo< R
(4) Let(an}n=o be a sequence in C. Define R-i-lim...
question 6 plz if you can do it fast ,, thank you
Feb 02 , 40.5, - 0 6 5. Define a Boolean function F : {0,1} → {0,1} by f(a,b,c) = (4a + 3b + 2c) mod 2. Find S (1,1,1) and f (1,0,1). 5. Let A = m, B=n with m, n finite numbers and m > n. Prove that for any function 1: A B./ is NOT 1 - 1 Let R be a binary relation defined...