Let K = Q(i) denote the field of Gaussian numbers. Note that 10 = (3 + i)(3 − i) = 2 · 5. Is this an example of non-unique factorization in Z[i]? Give reasons for your answer.

Q: Find the Fourier expansion of f(x) = 3–x ; 0<xs 2n; |D

A:

Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0

A:

Q: (a) Find the Fourier transform of the function g: RR defined by Ste-kt, for t > 0, g(t) = otherwise.…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the Fourier transform off (x) defined by Example 6. 1, |x| a f(x) = sin s ds (ii) 00 sin sa.…

A:

Q: Determine the Fourier-Bessel expansion in the functions J0(λkx) of f(x) = x2 on the interval (0,1).…

A:

Q: Use Laplace transforms to solve the following initial value problem. x"-25x 9t; x(0)=x'(0) = 0 %3D

A: Given: Given IVP is x''-25x=9t,x0=x'0=0 To find solution of IVP we use Laplace transform

Q: Find the Laplace Transform of the following: 4) e3z-2bt  (variables other than t are considered…

A:

Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 3o otherwise Find the Fourier transform of (x if 0 <х<а lo otherwise f(x) =

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Find the Laplace transform of erfc (1/√t).

A: Complementary Error Function:       "erfc is the complementary error function. The complementary…

Q: a k 2 + k² S 2 + k² k

A:

Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

Q: Given f(x)=6*x^3+6*x^2+-4*x, identify the two critical values. Put the most positive critical value…

A:

Q: Use Laplace transforms to solve the following initial value problem. x'' - 9x = 5t; x(0)=x'(0)=0…

A: The given initial value problem is x''-9x=5t, x(0)=x'(0)=0 The laplace differential formula is…

Q: Calculate the Fourier transform of f(x) = (1 – 2)e-(z-a)?/2_

A: Calculate Fourier transform of e-x-a2/2:  ∫-∞∞e-x-a2/2·e-jωxdx=e-jaω∫-∞∞e-x-a2/2·e-jωx-adx-a…

Q: 2 1. Prove that L(2) S

A: To prove L2=2s

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS: F(t) = for…

A:

Q: Consider a function f(t) with a finite discontinuity at t = 0. Given that its Fourier transform is…

A:

Q: Solve the following problem given that the scalar field f = xy? + 3xiz². Find Vf at point (8,1 -2).…

A:

Q: what is the Fourier transfrom of the following 0.5 d²x(t) j2nf dt2

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: 1 Determine the inverse Laplace transform of (s–2)(s-3)

A:

Q: Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0<x< TI f(x) =

A:

Q: Q4 Fined a Sp litting field of xt_2.( show your work) (a) aver Q

A: a) Over ℚ The degree of fx=x4-2 is 4, so the splitting field K of f(x) must contain its 4 roots.…

Q: show that: n L{t"-1eat} S - a L{t"eat} By using the definition of the Laplace transform

A:

Q: Determine the inverse Laplace 2s +3 transform of (s+4)

A:

Q: (d) Show that the Fourier transform of a Gaussian is a Gaussian, and hence show that eik dk 2πδ(x).

A: The Dirac delta function is one of the most significant functions in mathematics. It is widely used…

Q: Consider the function S e20x+2, if x 0 The Fourier transform of f, defined by F(f)(§) := f…

A: Integral 0 to infinity the function must be zero. So only - infinity to 0, the integral exist.

Q: 3. Find the Fourier Transform of f(t) = 0, - osts0 le-at, osts ∞ a is positive constant

A:

Q: Obtain the Z transform of 10 s(s² +s+2)

A: We are given the Laplace transform fs=10ss2+s+2=51s-s+1s2+s+2=51s-s+12s+122+722-12s+122+722 So,…

Q: From Rogawski ET 2e section 8.4, exercise 1. Calculate the Taylor polynomials T2(x) and T3(x)…

A:

Q: a) Find the finite Fourier cosine Transform of f (x) = x² in 0 < x < 4.

A:

Q: Obtain inverse Laplace transform 1. (s+2)

A: Given expression is e-4s+23.

Q: 2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT (a) ifx[n]…

A: Given x[n]⇔DTFTXejω then we have to show x[n-n0]⇔DTFTXejωe-jn0ω=Z(ejω) (say) Proof: we have…

Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0 Thanks

A:

Q: 1. Compute the Fourier transform of the following signal: x(t) = e-3|t| sin(2t)u(t)

A: Hint: The convolution theorem of Fourier transform states that, the Fourier transform of the…

Q: 7 Find the inverse Laplace transform of using Residue theorem. (s+3)(s²+5s+6)

A:

Q: find the inverse laplace transform of; a)  (S^2+1)/S(S-1)(S+1)(S-2)

A:

Q: (B) Compute the discrete Fourier transform of g = t+1 on [0, 4) with length 3. F{8} = (C

A: To calculate the discrete Fourier transform of the below function on [0,4) with length 3. g=t+1

Q: 2. Compute the Fourier Transform of f(x) = e¬ax²

A:

Q: OR Find the complex Fourier transform of the convolution of f(x)= [3, -1<x<1 0, elsewhere, g(x)= X,…

A:

Q: Solve the following problem given that the scalar field f = xy? + 3x3z?. Find Vf at point (8,1, -2).…

A: Given function is, f=xy2+3x23z2  Now, calculating ∇f…

Q: 1. Find the Laplace transform of eat and 1 for t is greater than or equal to zero.

A: Given: e-at and 1 To find the Laplace transform of the given expression.

Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: Q2/ Find the Fourier expansion of the Periodic function whose de finition in one Aeriod is : Fo =…

A:

Q: Find the la place transform of (e²=²+) le. e-e 2

A:

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A:

Q: 3. In class it was said that 'the chain rule is the most important rule within differential…

A:

Q: 3. Determine the inverse Laplace transform of the following using the convolution theorem: 4 s²(S-2)

A: