ma1201-transformsandpartialdifferentialequations.PDFVIP

MA1201-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MATHEMATICS ACADEMIC YEAR – 2011 – 12(ODD SEMESTER) QUESTION BANK SUBJECT CODE/NAME: MA1201-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS YEAR/SEM: II / III UNIT I FOURIER SERIES PART – A 1. Explain periodic function with two examples. 2. State Dirichlets condition 3. To which value,the half range sine series corresponding to f (x) x 2 expressed in the interval (0,5)converges at x=5? 4. If f(x) = eax is expanded as a Fourier series in (0,2π) ,what is the value ofb ? n 5. Does f(x) = tan x posses a Fourier expansion? 6. Obtain the value of a in the Fourier expansion of f(x) = 1cos x in (0,2π) 0 2x 7. In the Fourier expansion of f(x)= 1 , - π x 0  2x = 1 , 0 x π in (-π, π).  Find the value of b the coefficient of sin nx. n, 8. Determine the Value of a0 of the function f(x)= sin x ,- x in the Fourier expansion. 9. If f(x) = x + x2 is expanded as a Fourier series in (-π,π), find the value of an . 10. Find the coefficient b5 of cos5x, in the Fourier cosine series of the function f(x)=sin5x in the interval (0,2π) 11. f(x) = x(2π-x) is expanded as a Fourier series in (0,2π). Find an 12. State the nature of the Fourier expansion of f(x) = xcosh2x in (-π,π). 13. Without evaluating any inte