Elective Applied Mathematics
BE Computer (PU) Semester 43 credit hours
Applied Mathematics
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a) Show that Z[nf(t)] = —z = [F (2), ] where F(z) = Z[f(9). " Zz Find Z Leateal b) Find the solution of one dimensional wave equation a? Ch aC er 7 — ‘ at =…PU Spring7) Express the Laplacian Vuesataz polar ; OR : Derive two dimensional heat equation completely with necessary assumptions. ; . b) Find the temperature in a…PU Spring8a) Find the Fourier cosine transform of f(x) = e ”™ form 0,and 7 then show that oS dx = Eek, 0 if x<0 co cos wx +w sin wx J + =0 b) Show that fy ——[2 dw=45 if…PU Spring8Attempt all the questions: 4x2.5 a) Check analyticity of f(z) =z”. b) Find Z(a”). c) Find the solution of the partial differential equation uy, + 9u = 0. d)…PU Spring