. ▁Fourier ▁transform s ▁involve ▁integr als ▁rather ▁than ▁sums , ▁and ▁are ▁used ▁in ▁a ▁similarly ▁diverse ▁array ▁of ▁scientific ▁fields . ▁Many ▁natural ▁laws ▁are ▁expressed ▁by ▁rel ating ▁rates ▁of ▁change ▁of ▁quantities ▁to ▁the ▁quantities ▁themselves . ▁For ▁example : ▁The ▁rate ▁of ▁change ▁of ▁population ▁is ▁sometimes ▁joint ly ▁proportional ▁to ▁( 1 ) ▁the ▁present ▁population ▁and ▁( 2 ) ▁the ▁amount ▁by ▁which ▁the ▁present ▁population ▁falls ▁short ▁of ▁the ▁carrying ▁capacity . ▁This ▁kind ▁of ▁relationship ▁is ▁called ▁a ▁differential ▁equation . ▁If , ▁given ▁this ▁information , ▁one ▁tries ▁to ▁express ▁population ▁as ▁a ▁function ▁of ▁time , ▁one ▁is ▁trying ▁to ▁" sol ve " ▁the ▁differential ▁equation . ▁Fourier ▁transform s ▁may ▁be ▁used ▁to ▁convert ▁some ▁differential ▁equations ▁to ▁algebraic ▁equations ▁for ▁which ▁methods ▁of ▁solving ▁them ▁are ▁known . ▁Fourier ▁transform s ▁have ▁many ▁uses . ▁In ▁almost ▁any ▁scientific ▁context ▁in ▁which ▁the ▁words ▁spectrum , ▁harm onic , ▁or ▁reson ance ▁are ▁encountered , ▁Fourier ▁transform s ▁or ▁Fourier ▁series ▁are ▁nearby . ▁ ▁Statistics , ▁including ▁mathematical ▁psych ology ▁ ▁Int elligence ▁quot ients ▁are ▁sometimes ▁held ▁to ▁be ▁distributed ▁according ▁to ▁the ▁bell - sh aped ▁curve . ▁About ▁ 4 0 % ▁of ▁the ▁area ▁under ▁the ▁curve ▁is ▁in ▁the ▁interval ▁from ▁ 1 0 0 ▁to ▁ 1 2 0 ; ▁corresponding ly , ▁about ▁ 4 0 % ▁of ▁the ▁population ▁scores ▁between ▁ 1 0 0 ▁and ▁ 1 2 0