Transforms and Partial Differential Equations

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Transforms and partial differential equationImportant questions1VEL TECH Dr.RR & Dr.SR TECHNICAL UNIVERSITYDepartment of MathematicsTransforms and Partial Differential EquationsSem:III Year :IIUnit :I FOURIER SERIESPart A(2 marks)1.Find the Fourier sine series for the function f(x)=1, 0 x < is32 sin cos2 .as as asS | ` . , Hence deduce that 30sin cos4t t tdtt Using parsevals identify show that,230sin cos15t t tdtt | ` . ,10. Evaluate 2 2 2 2dx(x +a )(x +b ) using Fourier Transform11. Find Fourier cosine transformer 2 2a xe and hence find 2 2a xsF [x.e ]12. Find the Fourier transform of a xe if a > 0.Deduce that 2 2 2 30( ) 4dxx a a+ if a > 0 [Anna May/ June 2003]13. Find the fourier Transform of f(x) 1 10, 1x in xin x