Questionbanks  MATHSIII (EXTC) 
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MODULE1 1. Evaluate Laplace transform of (Given any Numerical). MODULE2 1. Find the inverse Laplace of (Given any Numerical) using Convolution theorem. 2. Solve Differential Equation with (Given any value) by using Laplace transform. MODULE3 1. Find the range Fourier sine series for f(x)= (Given any Numerical) 2. Show that the set of limitations (Given any value) Is orthogonal over (Given any value). Hence construct orthonormal set of functions. 3. Find the fourier series for (Given any Numerical). 4. Find the fourier transform of f(t)= (Given any Numerical) 5. Find complex form of the fourier series for f(x) =(Given any Numerical) where ‘a’ is a real constant. Hence deduce that (Given any Numerical) 6. Find fourier cosine integral representation for (Given any Numerical) MODULE4 1. FInd the directional directive of (Given any Numerical) 2. Find a unit normal to the surface (Given any Numerical) 3. 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). 4. Find Ф if (Given any Numerical) and also evaluate (Given any Numerical) along a curve joining the points. MODULE5 1. Using Gauss Divergence theorem (Given any Numerical). 2. Evaluate by Green’s theorem (Given any Numerical). MODULE6 1. Determine the constants. (Given any value) is analytic. 2. Show that (Given any value) is a harmonic function. Also find its harmonic conjugate. 3. Find orthogonal trajectories of the family of curves (Given any Numerical) 4. Bessel Function (Given any Numerical) 5. Find an analytic function f(z) whose imaginary part is (Given any Numerical) 6. Find bilinear transform that maps. (Given any Numerical) Find invariant points of this transformation. 
