Pokhara University
Bachelor of Engineering in Computer Engineering
Semester 4 · PU Spring
Course Title: Applied Mathematics
Full Marks: 100Pass Marks: 45Time: 23 hrs.
Candidates are required to give their answers in their own words as far as practicable.
- 4.7
- 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 = eS with initial velocity g(x), initial deflection f(x) and : boundary condition u(0, L) = 0 = u(L, t). ‘ : d atu , eu 5 coordinates.
- 5.8
) Express the Laplacian Vuesataz polar ; OR : Derive two-dimensional heat equation completely with necessary assumptions. ; .
- b) Find the temperature in a laterally insulated bar of length Lwhose ends are kept at temperature 0, assuming that the initial temperature L x if 0< x<> is f(x) = L A L-x if 3<*< L f Sea
- 6.8
- a) 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 x=0. ne* ifx>0
- 7.
Attempt 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) Define linear partial differential equation with suitable example. SS DD
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