MA8353 Important Questions Transforms and Partial Differential Equations

MA8353 Important Questions Transforms and Partial Differential Equations Regulation 2017 Anna University free download. Transforms and Partial Differential Equations Important Questions MA8353 pdf free download.

Sample MA8353 Important Questions Transforms and Partial Differential Equations:

1.State Dirichlet’s conditions.
Solution: Any function f x can be develop as Fourier series a n x b n x a
where
n n a ,a , b 0 are constants, Provided it satisfies the following Dirichlet’s condition.
(a) f x is Periodic ,single valued & finite
(b) f x has a finite number of finite discontinuities in any one period & number infinite discontinuity.
(c) f x has at the most a finite number of maxima & minima

2.State tan x whether can be expanded as a Fourier series .It so how? If not why?
Solution: tan x cannot be expanded as a Fourier Series .Since doesn’t satisfy Dirichlet’s conditions.( tan x
has infinite number of infinite discontinuities)

MA8353 Important Questions Transforms and Partial Differential Equations

3.Find the constant term in the expansion of 2 x cos as a Fourier series in the interval ( , ) Solution: W.K.T2
1 cos2 cos2 x x 

4. Find the Root Mean Square value of a function f x over the interval (a, b)
Solution: The root mean square of f x over the interval is defined as R.M.S =
b af x dx ba MA8353 Important Questions Transforms and Partial Differential Equations

5.Find the Root Mean Square value of f (x)  x , 0  x  l 2
Solution: The root mean square of f x over the interval is defined as R.M.S =
6.Give the expression for the F.S co-efficient n b for the function f (x) defined in (-2,2)

8. What is meant by Harmonic Analysis.
Solution: The process of finding the F.S for a function given by numerical value is known as harmonic
analysis. In the harmonic analysis the Fourier coefficients a , an &bn MA8353 Important Questions Transforms and Partial Differential Equations

Subject name	Transforms and Partial Differential Equations
Semester	3
Subject Code	MA8353
Regulation	2017 regulation

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