Questionbanks  MATHSIII (Electronics) 
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MODULE1 1. Solve Exact Differential (Given any Numerical) with (Given any value). 4. Find Laplace transform of (Given any Numerical) MODULE2 1. Find the inverse Laplace of (Given any Numerical) using Convolution theorem. MODULE3 1. Find the range Fourier sine series for f(x) = (Given any value) 2. Obtain Fourier series for f(x) (Given any Numerical) Hence deduce that (Given any value) 3. Show that the set of limitations (Given any value) Is orthogonal over (Given any value). Hence construct orthonormal set of functions. MODULE4 1. FInd the directional directive of (Given any Numerical) at the point (2,1,1) in the direction of the vector i+2j+2k. 2. Show that (Given any Numerical), is a conservative field. Find its scalar potential and also find the work done by the force (Given any value) in moving a particle from (1,2,1) to (3,1,4). 3. Prove that (Given any Numerical) Is irrotational and find scalar potential. MODULE5 1. Using Gauss Divergence theorem, evaluate (Given any Numerical) and S is the cube bounded by (Given any Numerical). 2.Evaluate by Green’s theorem for (Given any Numerical) where C is the rectangle whose vertices are (Given any value) 7.Use Stokes theorem to evaluate (Given any Numerical) and S is the surface of hemisphere (Given any value) lying above the XY plane MODULE6 1. Determine the constants a,b,c,d,e if f(z)= (Given any Numerical)is analytic. 2. Prove that Bessel Function. (Given any Numerical) 3. Show that under the transformation w= (Given any Numerical), real axis in the zplane is mapped onto the circle w=1. 7.Show that (Given any Numerical) is a harmonic function. Also find its harmonic conjugate. 9.Find an analytic function f(z) whose imaginary part is (Given any Numerical) 12. Find the Bilinear transformation which maps the points z=1, i,1 onto the points w=i, 0i. 13. Find the orthogonal trajectories of the curves (Given any Numerical) where (Given any value) is a real constant in XY plane. 14. If (Given any Numerical) find analytic function whose real part is u. 
