Please can u send the solution of these problems please it will be great help plzz I request u to send all the question solutions plzz .you can send the solution one by one plzzzz 11. a) Find the analytic function f(z)=u+iv, if u-v = (x – y\x² + 4.xy+ y² ).15. A homogeneous rod of conducting material of length 100 cm has its ends kept at0SxS 50(11b) Evaluatesin z+ coS TZ-dz where C is the circle z= 3.x,(z – 1)(z – 2)zero temperature and the temperature initially is u (x, 0)=100-x 50sIS100Find the temperature u(x,1) at any time.12. a) Find Laurent's expansion of7z- 2z(z+1)(z – 2)x²b) Evaluate +1)x* + 4)f(2) =in the region 1<|z+ 1|< 3.16. a) Find the bilinear transformation which maps the points z = 1, i,-1 onto the points'E > + z|> 1w = i,0,-i.8.dx.b) Evaluatedz where C is the circle |z – 2| = ÷.(z- 1Xz- 2)13. If f(x)=cos x), expand f(x)as a Fourier series in the interval (-,7).-2-2e2* +3x y.%3D17. a) Solve14. a) Solve (x? - y² - z² )p+ 2xyq = 2xz.b) Solve 2z + p² + qy+ 2y = 0 by using Charpit's method.%3Db) Find the complete solution of z (p² +q° )= x² + y²,3%3D13 a) Find the Fourier series expression of f(x) = x + x, -T S X ST.1Deduce that 1+1122 32 42b) Obtain the half range Fourier sine series for f(x) = 2x – 1,0 < x < 1.14 a) Obtain the general solution of 2xzp + 2yzq + x² + y - z? = 0.b) Solve p + q = pq by Charpit's method.11 a) Show that the function u(x, y) = 4xy - 3x+2 is harmonic and find its conjugate%3Dharmonic function v(x, y).15 Solve the Laplace equation-,2dy= 0 for a rectangular plate subject to the followingz-1b) Apply Cauchy's integral formula to evaluatedz, where C is |z-i| = 2.(z+1)2 (z- 2)conditions.U(x, 0) = u(x, 1) = 0, u(0, y) = y andди- (1, y) = -5z2 -112 a) Expand f(z) =in the regions (i) Iz| < 2 and (ii) 2 < |z| < 3.(z+2)(z+3)16 a) Find the analytic function f(z) such that Re[f (z)] = 3x² – 4y – 3y² and f(1+i) = 0.%3D%3D2xb) Evaluate|1+2 cos0de.b) Find the bilinear transformation which maps the points z = 1, i, -1 into w = i, 0, -i andhence find the image of |z| <.1.5+4cos017 a) Solve [2D² – 5DD' + 3(D')² +D- D'] z = e*y.TCCoscoscos8b) Show that |x| = 1---2 < x < 2.%3D3252TC1604 11 (a) Find the analytic function f (z) = u + iv where u(x, y) =e* (xcosy - ysiny). 26z2 +z(b) Evaluate 02dz where C is the circle z-1= 1.z2 -1|12 (a) Expand f(z)=1in a Laurent series valid for (i)13(z +1)(z+ 3)dx(b) Evaluate„(l+x²)?14 (a) Solve z(p-q)=z²+(x+y)²(b) Solve 2(z + xp + yp) =yp2 by using Charpits method.du15 Find the solution of the heat equationa²u00 subject to the conditionatu(0, t) = 0 = u(?, t) and u(x, 0) = &x - x².Əx²16 (a) Find the bilinear transformation which maps the points 1, i, -1 onto the points6040,1,00.(b) Evaluate (cos(2°) where C is the circle z=2cos(z')(z +1)?17 (a) Solve (D² + DD' – 6D² ) = y sin x-(b) Find the complete and singular integrals of z = px + qy - 2 pq

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Description: Please can u send the solution of these problems please it will be great help plzz I request u to send all the question solutions plzz .you can send the solution one by one plzzzz 11. a) Find the analytic function f(z)=u+iv, if u-v = (x – y\x² + 4.xy

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Answered: 11 (a) Find the analytic function f (z)…

Math

Advanced Math

11 (a) Find the analytic function f (z) = u + iv where u(x, y) =e* (xcosy - ysiny). 6z +z (b) Evaluate dz where C is the circle z-1= 1. z -1 C.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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