Laplace Transform 6.1

Power Series0 n2 an X Atxn o

Acn x Atx Acn An A 0 1 2,3

EI Acn I x It x 1 21 3 1

Atx for 1 1 1

am n if Axt t t

Atx ex for all XER

Continuous analogue

h O l 2 3 mis t Zo

Aln ffta

Ei Son o

E.ioanxn Atx fffit xtdt Fox

Xt een It eGenx t S't

e lax S

Laplace Transform

for all s sitJeff it e Stolt Fls L fHI the integral is defined

Aside Fourier transformfCt Flw Effete

i wt

t time w frequency

Applications of Laplace transform

Solving diff egn's

Probability

L probability distributionfunction

moment generating function

Statistical Physics

I densityof statefunction Epartition function