Transcription of table of laplace transforms - Educating Global Leaders
1 table of laplace transforms1ft()fs()tnn=1,2,..s>0 n!sn+1 1s2 t ta a>-1 Ga+1()sa+1s>0 eat teat tneat 1s-a 1s-a()2 n!s-a()n+1 s>a s>a s>a t 0 sinat cosat tcosat tsinat as2+a2s>0s>0 ss2+a2 2ass2+a2()2s>0s>0 s2-a2s2+a2()2 eatsinbt eatcosbt bs-a()2+b2 s-as-a()2+b2 s>a s>a sinhat coshat tcoshat tsinhat eatsinhbt eatcoshbt as2-a2 ss2-a2 s>a s>a s>a s>a 2bss2-a2()2 s2+b2s2-a2()2 bs-a()2-b2 s-as-a()2-b2 s>a+b s>a+bmaple ut-a()=0t<a1t a a>0s>0 e-assft() t 0fs() dt() 1 dt-a() e-as a 0 s>0s>0s>0 J0at() J0at() tpJpat() p>-12 s>0 s>0 s>0 1s2+a2 2papGp+12 ps2+a2()
2 P+12 e-a24ss pGk()t2a k-12Jk-12at() pGk()at2a k-12Jk-32at() k>0 k>12 1s2+a2()k ss2+a2()k s>0 s>0 erfat() erfat() erfca2t a>0 a 0 a 0 a>0 e-a2t2 1ses24a2erfcs2a s>0 ass+a2 s>0 1se-as s>0 p2aes24a2erfcs2a s>0 laplace transform is calculatedwith the command laplace (f(t),t,s):f(t) denotes the function to be transformed, t is the independent variable of the function,s is the variable of the transformed functionFor calcualtaion of laplace transformor inverse laplace transform the package with integral transforms has to be downloaded:> with(inttrans); [fourier, laplace ,invlaplace.]
3 ]Example 1:> laplace (t^2,t,s); 2s3> f(t):=t^2*sin(5*t);Example 2:> laplace (f(t),t,s); f(t):=t2sin(5t) 1-at()e-at ss+a()2 Jnat() s2+a2-s nans2+a2 n=0,1,2,.. 103s2-25()s2+25()3 Inverse laplace transform is calculatedwith the command invlaplace ( (s),s,t): (s) denotes the function to be transformed, s is the independent variable of the function,t is the variable of the transformed function f f> phi(s):=exp(-4*s)/s;Example 3:> laplace ( (s),s,t); f fs():=e-4s()s Heaviside(t-4)> phi(s):=exp(-3*sqrt(s));Example 4:> laplace ( (s),s,t); f fs():=e-3s() 3e-94t 2pt32() 1s
