If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't know how to get that.

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 L-1 1)…

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Q: The Z inverse of 3z/(z-2) is:

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Q: 1. Consider the following first-order ordinary differential equation 2,2 2x²y cos x dy + (2xy² cos x…

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Q: Exercise 4.22. Suppose K is a continuous function on R that is zero for all 02. Assume f |K(0)| d0 =…

A: Given: K is a continuous function To find: Solution

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Q: B)Evaluate the integrals: i) it) ¹-² dxdy, 2/2 finx 2² dz dy dx.

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Q: 1. Write the solution of the system of equations: P₁ = 5p₁ - 4p₂ + e²t; p2 = P₁; P₁(0)=P₂ (0) = -11

A: Given system of equations are p1'=5p1-4p2+e2t,    p2'=p1   Also given p1(0)=32,   p2(0)=-11   To…

Q: 1) Using Laplace transform methods, solve for t20 the following simultaneous differential equations…

A: Given simultaneous differential equation is dxdt+dydt+y=tdxdt+4dydt+x=1 With condition x(0)=1,…

Q: 2. Prove that if alc and a + b = c, then alb. 3. Show that if 2a + 1 is a multiple of 5, then 14a² +…

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Q: 30Find the Laurent Series of 3 flz 1: J = C:/Z/=1 (2-1)2 (2-3)

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Q: if (1+i)(x+iy) = 2+4i then 5x is: * O 15 O 10 05 O 3 Let z be a complex number such that |z| = 4 and…

A: Given (1+i)(x+iy)=2+4i. We find 5x.

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Q: Solve by the Lapace Transform: y(t) + 4 y(T) (t-T)dt = 2t ²

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Q: Reversing the order of integration fxsinydydx.

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Q: a. Solve the ODE y" + 3y + 2y = 0. b. Use the method of undetermined coefficients to find a…

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Q: Exercise 2 Using the Laplace transform and showing the details, sovle the IVP y" + 3y + 2y: { 1 if…

A: We have to apply the Laplace transform.

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

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Q: has solutions of the form R(p) etmzting whe

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Q: : Find the divergence of the vector field the point (2,4,1). y F(x, y, z) = x² √yi + =j+zk

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Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute the polor integral…

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Q: -<t <-/ Let f(t) be defined as f(t) = t -<t</ TU TC <t<n Extend f(t) periodically and find the…

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Q: Determine if the series converges or diverges; if the series converges, find its sum. Σ 20+1 6h-1…

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Q: Q2: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý-y=e*

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Q: Find with sketch the Fourier coefficients and Fourier series of the function fx) defined by f(x)= x²…

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Q: / Reversing the order of integration fxsinydydx.

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Q: Prove Bernouilli's Inequality which states: If x ≥ −1 then (1 + x)” ≥ 1 + nx for all natural numbers…

A: To Prove: Bernoulli's Inequality which states: If x≥-1, then (1+x)n≥1+nx for all natural numbers n

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Q: A skydiver weighing 176 lbf (including equipment) falls ve 12 s of free fall. Assume that the force…

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Q: 1- Solve dx = cos x + y, where y = 2.0 at x 0 take step size h = 4x = 0.1 and solve for 0 ≤ x ≤ 0.2…

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Q: :y= x,y = 2x2 − 3x

A: To find centroid we need to find area bounded A between curves  then centroid x =∫abx×fxdxAy…

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Q: 7. Find the eigenvalues and eigenvectors the system X' = Use the eigenvalues and eigenvectors to…

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Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

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A: Given: S=200x5+y+100y10+y To find: Solution