The nonlinear system 5a – x3 = 0, x2 – 0.25(sin x1 + cos x2) = 0 has a solution near (, )'. (a) Find a function G and a set D in R? such that G : D →→ R² and G has a unique fixed point in D. (b) Apply functional iteration to approximate the solution to within 10-5 in the l∞ norm.

Q: 1 2) Find the linearization at x = a and use it to approximate f(b). f(x) = a = 6 b = 6.1 V4x+1 f(x)…

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Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3) (2z…

A: 3. Given function is 2z+1zz3-5.

Q: Write the system y1 = -y1+2 cos(r)y3 + e 2 = xy1 - 10y2 + e" y3 +20 sin(x) Y3 = e2" y2 – a²y3 %3D…

A: The matrix form of given system of differential equations as follows

Q: hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x.…

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Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

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Q: Assume that y, (1) = e and y, (1) = e" form a fundamental set of solutions. (b) Let y3 (t) = -4e2 Ya…

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Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3)…

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Q: nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an…

A: see my solution below

Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

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Q: 4) Find the Hermitian form [18] [2] X = H= XTAX where

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Q: Let f(x) = (x – b) Ax + c, where A is symmetric and positive definite matrix, b is a vector and c is…

A: Given that  f(X)=X-bTAX+c, where A is symmetric and positive definite matrix, b is a vector and cis…

Q: b) Solve ди Ət ди +3x = 1+u, Әх -8AHAB, u(x,0) = f(x). t > 0,

A: Given pde is  ∂u∂t+3x∂u∂x=1+u,  -∞<x<∞, t>0 and u(x,0)=f(x) we have to solve this pde

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (2² + 3z – 5)/z3 (3) (2z…

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