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Here I am giving you question paper for PTU B.Tech EE-3rd Sem-Applied Mathematics-III (AM-201) Examination B.Tech. (Sem. - 3rd/4th) , MATHEMATICS- III (AM -201) Time: 03 Hours Section -A Ql) (10 X 2 =20) a) Canf(x) = tan x be expanded as a Fourier series in the interval-(-rc,rc). b) Give the sufficient condition for the existence of Laplace transform of f(t). ' f.c } 1 1 . ' c) If Lv (t) =- e-s , find the Laplace transform of e-t f(3t). d) Find the D1 es2 . e) Write algorithm ofpow,er series method for solution of differential equations. £) For the Bessel's function prove the recurrence relation ~ ~p J p (x)}= xP J p-I(X). g) Form the partial differential equation from F(xy + Z2,x + y + z) = O. h) Is the function u(x, y) = 2xy -+-3xy2 - 21, a harmonic function? i) Give the definition of Conformal transformation. Given that x(O)= 2, y(O) = 1.. \ Q3) Using convolution theorem find the inverse of ~ Q4) Find the §eries solution of differential,equation (1 - X2) y" '- 2x y' + 6y = O. Q5) Solve (D: - D: Dy + 2D~ D.: - 5D, D~ + 3D~)z = o. Q6) Evaluate fIzl2 dz, around the square with vertices at (0,0), (1,0), (1,1) Q8) Solve Laplace's equation in rectangle with u(O,y) = 0, ¥(a, y) = 0, ~(x, b) = O. . and u(x, 0) = f(x). . 1 Q9) Find the Laurent series off(z) = ( )( 2) for the following intervals ![]() ![]()
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Applied Mathematics gives the basic concept of electrical circuits to the student. At Punjab Technical University, this subjectcomes in 3rd semester. Paper pattern Maximum marks of this paper-100. There are 3 sections. First section contains 10 shirt questions. All of them are compulsory. They contain 2 marks each Second section contains 5 questions. Out of those 5, a student needs to attempt only 4. Each question carry 5 marks each. In the last section, there are 3 questions which consist of many sub parts. Of these 3, only two questions need to be attempted. Each question carries 10 marks. Question Paper ![]() ![]()
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