Engineering BE Electronics and Computer Science Sem 3 December 2019 2019 Applied Mathematics Question Paper - Mumbai University | munotes
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Questions asked in this paper
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Q1 Question No.1 is compulsory
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Q2 Attempt any THREE of the remaining
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Q3 Figures to the right indicate full marks
- A) Find Laplace transform of f(t) =
- B) that y” is harmonic function also find corresponding analytic 5
- C) Find the half range sine series of f(x) =2x ,7) 5
- D) Find the Unit normal vector to the surfaces x? +z? =9 and z=x? +y?-3 at 5 (2,-1,2) hence find angle between them Prove that J(-3/2) (x)= - A +sinx)
- B) Find the Bilinear transformation which maps the points z = -1 onto the 6
- C) the fourier series for f(x) =xcosx 8
- A) Find inverse laplace transform of 6
- B) Show that the of functions {cosx COS5X 18 an orthogonal 6 over 2/2] .Hence construct orthonormal set of functions
- C) that y = Vx Jn(x) isa solution of the equation , 8
- A) Prove that f = — 6
- B) Gauss’s Divergence theorem to evaluate > N.Fds where F=4xi +3yj 6 2zk and S is the surface bounded by x=0 ,y=0 ,z= 0 and 2x +2y +z=4
- C) Solve using Laplace transform( D? +2D+1)y ,given y(0)=4 and 8 A Find Fourier series for 6
- B) Find the image of the region bounded by x+y=0 , x=y , x+y=1 under 6 the bilinear transformation w +2i Prove that + is a conservative field 8 Find (i)Scalar Potential for F The work done in moving an object in this field from (0 ,1-1)
- A) Find the Laplace Transform of e* f sin3ucos2udu 6
- B) Find Complex form of Fourier Series of sinh2x in (-2 , 2) 6
- C) Express the function 8 f(x) ={ as Fourier integral .Hence evaluat
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