We are given the following heat equation on a 1-dimensional ring. D It has periodic boundary conditions u(−1,t) = u(1,t), ur (−1,t) — uz (1,t) with initial condition u(x, 0) = x² (1) Express the solution as a series form. (2) Determine the coefficients of the series. (3) Plot the solution using a sufficient number of terms from the series.

Q: Half range Fourier Series: 3. Determine the half-range sine series for the function defined by:…

A:

Q: Find the projection of 6 = -3 -3 -3 onto the image of A = 1 0 3. 0 14.

A: To find the projection

Q: = 8-2 s² +48 +5 4s

A:

Q: Verify that the vector X, is a particular solution of the given nonhomogeneous linear system. 2 1 X'…

A:

Q: Complete each statement by filling in each blank with the correct word or phrase to give it a…

A:

Q: An 8.5 metre-wide pool is 4.5 times longer than it is wide. If you were to swim diagonally across it…

A:

Q: = qCxwid xpxsav{" Tuls कछ कि = गई {of}- htধ = {ई} द { (x+2)qx c) Step 3

A:

Q: Miley rides her wrecking ball during leisure. On a Wednesday, she swings an initial arc distance of…

A: Initial swing : 25 m With each succeeding swing, she travels along an arc that is three quarter as…

Q: Use the Laplace transform to solve the given initial-value problem. v = s(t − ½ n) + s(t – 2/2),…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Using the Fourier integral representation of the function a, x |k| we find = S TT JO where a=9,…

A: Answer given below.

Q: 8. A patient is given a dosage Q of a drug at regular intervals of time T. The concentration of the…

A: Given that,  the concentration of the drug in the blood is: dCdt=-keC Reaarange the terms on both…

Q: phism, where R is a commutative ring with unity. Le he arbitrary elements of R. Then there exists a…

A:

Q: 3. Suppose k = 0.01 hr¯¹and T = 10 hr. Find the smallest n such that Rn > 0.5R.

A:

Q: ow many conjugacy A5 have ? Define characters of A5 breifly .

A:

Q: 1. A function cannot have a relative extremum and a point of inflection at the same point in its…

A:

Q: Consider the second-order system of differential equations d²x dt² d'y dt2 =x+3y, The coefficient…

A:

Q: (a) Why does the sequence of real numbers fn(x1) necessarily contain a convergent subsequence (fnk…

A: To Explain: Why does the sequence of real numbers fnx1 necessarily contain a convergent subsequence…

Q: X dy dx - Y 2 x arcsin (r)y5

A: CONVERT THE GIVEN EQUATION IN LINEAR EQUATION OF FIRST ORDER BY SUBSTITUTING v=1y4 AND THEN SOLVE…

Q: Given the function f(x) = 2x³ - 3x² - 72x + 2, determine the intervals where the function is…

A:

Q: Xi -1 0 1 Yi 7 35 19t9h

A:

Q: Find the divergence of the field. F = (-2x+2y+3z)i + (8x - 2y - 5z)j + (6x + 8y - 7z)k div F =

A: Divergence of the field F is  ∇.F=∂∂xi+∂∂yj+∂∂zk.F

Q: . Let H be the set of all points (x, y) in R² such that x² + xy 3y² = 3. Show that H is a closed…

A: Given That : Let H be the set  of all points x , y in R2 such that x2+xy+3y2=3 or x2+xy-3y2=3. Show…

Q: 2 f(x) = x - x², g(x) = 3x - 1 and h(x) = = Determine an expression in simplest for for…

A:

Q: b) Calculate the derivatives of y = = 3x² + 2 and y = cos x — sin x c) Calculate the integrals…

A:

Q: Consider the sets A = {1, 2, 3, 4} and B = {a, b, c, d}, and the relations σ = {(1, b), (2, c), (3,…

A:

Q: Part B please

A:

Q: k.11 ad h

A: we get remainder 5

Q: Find the primary decomposition of A= 1 0 0 as a map from Q' to itself. 010

A: As per the question we are given a 3×3 matrix A and we have to find its primary decomposition as a…

Q: H = {[x ут X||X, Y |x, y ez} EZ

A: We use the property 1x.x=x and then to find M2x2

Q: A cone will be inscribed in a sphere of radius 10 in. Part A: Find the exact dimensions of the cone…

A: We will find volume of the cone in single variable and then maximize it by using 2nd derivative test…

Q: Question 4. The Fourier transform of f(t) is F(w) = 5e-3jw wj 8 4+ Using the Convolution Theorem,…

A:

Q: In a box 52 playing cards are there. Three events X, Y, and Z happen as follows: Event X is defined…

A:

Q: Choose the best option that answers each problem. You may choose only one. 1) Let R be the set of…

A: To Choose : The best option that answers each problem.Let R be the set of all subsets of a set X.…

Q: Prove the statement. Let f : A → B . If X ⊆ A, Y ⊆ B , and f-1[Y] = {x ∈ A|f(x) ∈ Y}, then f[X] ∩ Y…

A:

Q: £.(+). for TS ts......... L 1 +² for of t.<I 2

A:

Q: To which polynomial Eisenstein's Criterion. o ver as Ain a A f(x) >9x10-6x³ +21x-18 B. g(x) = x - 4x…

A:

Q: Given the data for the transportation problem in Table 12.21: (a) Use the northwest corner method to…

A: The solution of the problem is calculated using North West Corner method as shown in the next step.…

Q: Use polar coordinates to find the volume of the given solid: Insider the sphere x² + y² + z² = 16…

A:

Q: What is the residual error ||r||2 for the least squares problem [1237] 1941 2417 711 1177 475 1 0 0…

A: Given, Let, A = 100010001-110-1010-11B = 1237194124177111177475   We have to find the Residual error…

Q: the solution not complete and not apply the condition

A: As per the question, we are given the following linear partial differential equation : y*ux + x uy =…

Q: Apply householder reflectors to find QR-factorization tt of A = [ 23 -1 ] such that A= QR when Qis…

A:

Q: Assume that, for each n, fn is an integrable function on [a, b]. If (fn) → f uniformly on [a, b],…

A:

Q: The figure shows a period of the curve y = f(x) called “cycloid”, given in parametric form by the…

A: As per the question we are given the parametric equation of a cycloid as : x(t) = t - sin(t)  ,…

Q: 3 0 ³√²₂x³e¹³ dyd- 923

A: ∫03∫x29x3ey3dydx Clearly to solve it integrating 'y' first is hard nut to crack, lets change the…

Q: 4.) Are vectors Linearly independent? 2 3

A:

Q: Example: f(x) = e*-4x² Use the bisection method on the interval [0,2] with po = 1. Find P₁, P2, P3.

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

A: Given the field F is                 F=4yi+(5-2x)j+(z2-2)k, and      S:r(ϕ,…

Q: 5. A machine produces a total of 12,000 bolts a day which are on average 3% defective. Find the…

A: Given Data: Let us consider the given data, P( defective)= 0.03=p n= 600.

Q: 11. If F(x)= COS C 1+ 4t2 dt, find F"(x)

A:

Q: The volume of the solid bounded below by the xy-plane, on the sides by p=1, and above by p=- = 5,4…

A: