การแปลงลาปลาส, ในทางคณ, ตศาสตร, งกฤษ, laplace, transform, อการแปลงเช, งปร, นธ, ใช, นอย, างกว, างขวาง, แสดงอย, ในร, displaystyle, displaystyle, mathcal, left, right, จะทำให, เก, ดความเป, นเช, งเส, นของ, งค, เป, นอาร, วเมนต, จร, จะแปลงไปอย, ในร, ปฟ, งก, โดย, เป,. inthangkhnitsastr karaeplnglaplas xngkvs Laplace transform khuxkaraeplngechingpriphnththiichknxyangkwangkhwang aesdngxyuinrup L f t displaystyle displaystyle mathcal L left f t right karaeplnglaplascathaihekidkhwamepnechingesnkhxng f t sungkha t epnxarkiwemntcring t 0 caaeplngipxyuinrupfngkchn F s ody s epnxarkiwemntechingsxn karaeplngniepnkarthafngkchnhnungtxhnungthisakhymakinkarichnganinthangptibti khufngkchn f t kb F s nncbkhuknintarang karaeplnglaplasthukichpraoychncakkhunsmbtithimnmikhwamsmphnthaelakardaeninkarkhxngfngkndngedim f t nnsxdkhlxngkbkhwamsmphnthkbkardaeninkarinrupkhxng F s karaeplnglaplasthukprayuktichinngansakhymakmaythiepnaenwkhidthangwithyasastr sahrbchuxlaplasnimacakchuxkhxngpiaeyr simng laplas phuthinakaraeplngniipichinthvsdikhwamnacaepnkaraeplnglaplasekiywkhxngkbkaraeplngfuriey aetkhnathikaraeplngfurieynnichinkaraekfngkchnhruxsyyaninohmdkhxngkarsnsaethuxnkhunsmbti aekikhkahndih f t aela g t miphlkaraeplnglaplasepn F s aela G s tamladb f t L 1 F s displaystyle f t mathcal L 1 F s g t L 1 G s displaystyle g t mathcal L 1 G s tarangtxipniepntarangkhunsmbtikhxngkaraeplnglaplasdanediyw unilateral Laplace transform khunsmbtikhxngkaraeplnglaplasdanediyw odemnewla odemn s hmayehtuphawaechingesn Linearity a f t b g t displaystyle af t bg t a F s b G s displaystyle aF s bG s samarthphisucnidodykhunsmbtikhwamepnechingesnkhxngkarhapriphnth priphnthphlbwkethakb priphnthkhxngxngkhprakxbyxykhxngphlbwknn xnuphnthechingkhwamthi Frequency differentiation t f t displaystyle tf t F s displaystyle F s F displaystyle F epnxnuphnthxndbaerkkhxng F displaystyle F xnuphnthechingkhwamthi Frequency differentiation t n f t displaystyle t n f t 1 n F n s displaystyle 1 n F n s rupaebbthwipkhxngxnuphnthxndb nth khxng F s xnuphnth Differentiation f t displaystyle f t s F s f 0 displaystyle sF s f 0 smmutiih ƒ epnfngkchnthixnuphnthid differentiable function xnuphnthxndbsxng Differentiation f t displaystyle f t s 2 F s s f 0 f 0 displaystyle s 2 F s sf 0 f 0 smmutiih ƒ mixnuphnthxndbsxngxnuphnthxndbid Differentiation f n t displaystyle f n t s n F s s n 1 f 0 f n 1 0 displaystyle s n F s s n 1 f 0 cdots f n 1 0 smmutiih ƒ mixnuphnthxndb n idpriphnthechingkhwamthi Frequency integration f t t displaystyle frac f t t s F s d s displaystyle int s infty F sigma d sigma priphnth Integration 0 t f t d t u f t displaystyle int 0 t f tau d tau u f t 1 s F s displaystyle 1 over s F s u t displaystyle u t khux fngkchnkhnbnidehwiisd Heaviside step function aela u f t displaystyle u f t khuxsngwtnakar convolution khxng u t displaystyle u t aela f t displaystyle f t karkhyayechingewla Time scaling f a t displaystyle f at 1 a F s a displaystyle frac 1 a F left s over a right kareluxnechingkhwamthi Frequency shifting e a t f t displaystyle e at f t F s a displaystyle F s a kareluxnechingewla Time shifting f t a u t a displaystyle f t a u t a e a s F s displaystyle e as F s u t displaystyle u t khux fngkchnkhnbnidehwiisd Heaviside step function karkhun Multiplication f t g t displaystyle f t g t 1 2 p i lim T c i T c i T F s G s s d s displaystyle frac 1 2 pi i lim T to infty int c iT c iT F sigma G s sigma d sigma karhapriphnthcakrathabnaeknaenwding R e s c displaystyle Re sigma c sungxyuinkhxbekhtkarluekha region of convergence khxng Fsngwtnakar Convolution f g t 0 t f t g t t d t displaystyle f g t int 0 t f tau g t tau d tau F s G s displaystyle F s cdot G s inniyamkhxngkarsngwtnakar erasamrthkahndih ƒ t aela g t mikhaepnsunyid emux t lt 0sngyukhkhxngcanwnechingsxn Complex conjugation f t displaystyle f t F s displaystyle F s shsmphnthikhw Cross correlation f t g t displaystyle f t star g t F s G s displaystyle F s cdot G s fngkchnkhab Periodic Function f t displaystyle f t 1 1 e T s 0 T e s t f t d t displaystyle 1 over 1 e Ts int 0 T e st f t dt f t displaystyle f t epn fngkchnkhab khxngkhab T displaystyle T klawkhux f t f t T t 0 displaystyle f t f t T forall t geq 0 epnkarrwmkarkhxngkhunsmbtikareluxnechingewlaaelakhunsmbtikhxngladberkhakhnitechingxrrth aekikhxacphbehnkarsakdchuxkaraeplnglaplasxyangxunechn karaeplnglaplas karaeplnglaphlas karaeplnglaphlas hruxichkhanahnawa phlkaraeplng karaeplngrup xangxing aekikhArendt Wolfgang Batty Charles J K Hieber Matthias Neubrander Frank 2002 Vector Valued Laplace Transforms and Cauchy Problems Birkhauser Basel ISBN 3764365498 Bracewell R N 2000 The Fourier Transform and Its Applications 3rd ed Boston McGraw Hill ISBN 0071160434 bthkhwamekiywkbkhnitsastrniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy khnitsastrekhathungcak https th wikipedia org w index php title karaeplnglaplas amp oldid 4809062, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
