Fourier integral representation of f(x) e^(-x) if x>0

-

 

sol:
Fourier integral representation of 
    
        
       
       
substitute (2) in (1) 
        
and
Is the integral representation of f(x)

verifying directly,
     
        
        


NOTE :


verifying indirectly ,
        
        
        
        
        


PDF COPY


Comments

Post a Comment

Popular posts from this blog

SSLC samacheer mathematics guide

-
Image
           1 RELATIONS AND FUNCTIONS                        EXERCISE 1.1                       EXERCISE 1.2                           EXERCISE 1.3                            EXERCISE 1.4                        EXERCISE 1.5 29/9/2020 every day I uploade the sum thanking you see you tomorrow share it  
Read more

TAM3B - Differential equations

-
Image
  ( x - y ) dx -( x + y ) dy =0 Exact Equation If the first order partial derivatives of M( x,y ) and N( x,y ) are continuous then M dx + N dy = 0 is an exact equation if and only if  ∂ M/ ∂ y = ∂ N/∂ x Hence to solve the exact equation  M dx + N dy = 0   Integrate M with respect to x keeping y constant Integrate those terms in N not containing  x  with respect to   y The sum of those two integrals equated to c is the solution. EXAMPLE 1 ( x^2-2xy+3y^2 )dx+(y^2+6xy-x^2 )dy=0 EXAMPLE 2 ( 2xy-sec^2⁡x )dx+(x^2+2y)dy=0 EXAMPLE 3 Find the value of ‘ n ’ for which ( x+ye^2xy )dx+nxe^2xy  dy=0    and solve it EXAMPLE 4 ( sin⁡ x. tan⁡ y+1)dx-(cos⁡x.sec^2⁡y )dy=0 EXAMPLE 5 ( e^y+1)  cos⁡ x  dx+e^y  sin⁡x  dy=0
Read more