Exercise 1. Find the residues at z = 0 of the functions ez sinh(z²) 1 1 26 Z + z3 ' 25 and also find the orders of poles at z = 0 for these functions.

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) - v sin(e) and yusin(0) + v…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: find its harmonic conjugateu andd find analytic funchionf(2)=utiV sätisfying the Indicated condition…

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Q: If w sinxcosy + 1, I = sint, y cost, then by chain rule when t = 7, Select one: O A. 0 О в. - соs(-…

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Q: The domain of the function 7 (t) = (In t, cos 2t, /t – 2) is

A: Given that function rt→=lnt,cos2t,t-2To find : Domain Solution: rt→=lnt,cos2t,t-2t>0,t-2≥0

Q: 6. e* cos 9x , e9× sin x Ans. = (-4 sin (8x) + 4 sin (10x) + 5 cos (8æ) – 4 cos (10)) e10z.

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Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: Based on the graph, make a conjecture about whether the circulation and flux of F = (y, - x) on <t≤…

A: Given :  F→=y, -xC:r→t=4 cost, 4 sint     π4≤t≤2π To find :  a. Circulation b. Flux

Q: IfT: R² R³ is a linear transformation such that -n the standard matrix of Tis 13 T([2])-[3] . and T…

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Q: 2x sinh ( − y) + 2axy, sinh (x – y) −3Vy − z ta, 62 Vy – Let C be the line segment from (−1, 1, 1)…

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Q: 6у" + 26у — 0, y(0) = 9, у (0) — 4.

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Q: Determine the value of the arbitrary constant C: e" (ev – )cosa )cosa dy el sin2x, y(0) = 1 Select…

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Q: II. Consider the function g defined by 9(z, y) = cos (7z/T) logg(z Do as indicated. In what…

A: We know that the gradient of the function g contains the two vectors, one in the direction of x-axis…

Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: -1 X Determine whether or not the function u = tan equation: ux+uy = 0. yy is a solution of…

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Q: 4. Determine the phase shift and the vertical displacement with respect to y = sin x for each…

A: Given problem:-

Q: Find pairs of solutions of Laplace's equation, =0, based on these complex functions (a) ze2, (b) z*:…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3 Substitute Z=x+iy in Ze2z…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.