Jun 18, 2010 #1 J jani baadshah Junior Member level 1 Joined May 27, 2010 Messages 18 Helped 3 Reputation 6 Reaction score 3 Trophy points 1,283 Location pakistan Activity points 1,373 can anyone solve this problem me please??question is attached pdf.please reply with the detail thanks in advance
can anyone solve this problem me please??question is attached pdf.please reply with the detail thanks in advance
Jun 18, 2010 #2 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 Apply "Residue Theorem". The example at Wikipedia is your problem ( Residue theorem - Wikipedia, the free encyclopedia ). Note: \[ \int_C \frac{e^{itz}}{z^2+1} \,\! {}\,dz=\int_C \frac{e^{itz}}{2i}\left(\frac{1}{z-i}-\frac{1}{z+i}\right)\,\!\,dz {}=\int_C \frac{e^{itz}}{2i(z-i)} \,\!\,dz\] because the pole at -i is outside C Last edited by a moderator: Aug 27, 2010
Apply "Residue Theorem". The example at Wikipedia is your problem ( Residue theorem - Wikipedia, the free encyclopedia ). Note: \[ \int_C \frac{e^{itz}}{z^2+1} \,\! {}\,dz=\int_C \frac{e^{itz}}{2i}\left(\frac{1}{z-i}-\frac{1}{z+i}\right)\,\!\,dz {}=\int_C \frac{e^{itz}}{2i(z-i)} \,\!\,dz\] because the pole at -i is outside C
Jun 19, 2010 #3 J jani baadshah Junior Member level 1 Joined May 27, 2010 Messages 18 Helped 3 Reputation 6 Reaction score 3 Trophy points 1,283 Location pakistan Activity points 1,373 how residue theorem can be applied? it is actualy inverse fourier transform
Jun 26, 2010 #4 J jani baadshah Junior Member level 1 Joined May 27, 2010 Messages 18 Helped 3 Reputation 6 Reaction score 3 Trophy points 1,283 Location pakistan Activity points 1,373 well i have solved the problem using exponential integral