PROOF OF PROPERTIES OF LAPLACE TRANSFORM (part 1)

0) PROOF OF SOME ELEMENTARY FUNCTION

1) FIRST SHIFTING PROPERTIES 

2) LINEARITY PROPERTY

WHERE "a" IS A CONSTANT 

PROOF OF LINEARITY PROPERTY

3) MULTIPLY BY T  PROPERTY

4) DIVISION BY T PROPERTY

PROOF OF DIVISION BY T

5) LAPLACE TRANSFORM OF DERIVATIVE

Proof of laplace transfrom of first derivative