Questionbanks  MATHSIII (Computer) 
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MODULE1 1. Find laplace transform of (Given any Numerical) 2. Find laplace transform of F(x) = (Given any Numerical) 3. Using Laplace transform Evaluate (Given any Numerical) MODULE2 1. Find Laplace Inverse (Given any Numerical) using convolution theorem. 2. Solve using Laplace transform Differential equation (Given any Numerical MODULE3 1. Find half range cosine series for f(x)= (Given any Numerical) 2. Obtain fourier series for following functions: (Given any Numerical) Hence deduce that (Given any Numerical) 3. Show that set of following functions (Given any Numerical) Form an orthogonal set in (L, L) and construct an orthogonal set. MODULE4 1. Is f(z)= (Given any Numerical) is analytic? 2. if (Given any Numerical) show that V and H Harmonic and Find the corresponding analytic function. 3. Find the bilinear transformation which maps the points 0, 1, 2i Of zplane onto the points 4i, , 0 resp. Of wplane. Also obtain fixed Points of the transformation. 4. Find that (Given any Numerical) is analytic and find its derivative. 5. Find the analytical function (Given any Numerical) 6. Find the orthogonal trajectory of (Given any Numerical). 7. Show that (Given any Numerical) maps the circle (Given any Numerical) into straight line (Given any Numerical) 8. Show that the function f(z)= (Given any Numerical) is analytic and find f’(z) in terms of z. MODULE5 1. Find the Ztransformation of (Given any Numerical) 2. Find inverse Ztransform of f(x)= (Given any Numerical) 3. Find the Z transform of (Given any Numerical) MODULE6 1. Find the equation of the line of regression or Y on X for the following data. (Given any Numerical) 2. Calculate the coefficient of correlation between X and Y from the following data. (Given any Numerical) 3. Fit a curve of the form (Given any Numerical) to the following data (Given any Numerical) 4. From 8 observations the following results were obtained (Given any Numerical) Find the equation of the line of regression of x on y and the coefficient of correlation. 5. Compute Spearman’s Rank correlation coefficient for the following data: (Given any Numerical) 6. Fit a straight line of the form y=a+bx to the following data and estimate the value of y for x= 3.5. (Given any Numerical) 
