Chapter 5 (Laplace)

Question 1

u(t) (Heaviside function)

Answer 1

1, t>0
0, t<= 0

Question 1

delta(t) (Dirac delta function)

Answer 1

0, t != 0
inf, t =0

Question 2

L{C}

Answer 2

C/s

Question 3

L{f(t)} (F(s))

Answer 3

int [0, inf): e^(-st) * f(t) dt

Question 4

L{t}

Answer 4

1/(s^2)

Question 5

L{t^n}

Answer 5

n! / [s^(n+1)]

Question 6

L{e^(-at)}

Answer 6

1/(s+a)

Question 7

L{sin(wt)}

Answer 7

w/ [s^2 - w^2]

Question 8

L{cos(wt)}

Answer 8

s/ [s^2 - w^2]

Question 9

L{u(t-a)}

Answer 9

[e^(-as)] / s

Question 10

L{delta(t)}

Answer 10

1

Question 11

L{delta(t-a)}

Answer 11

e^(-as)

Question 12

L{erf(t/2a)}

Answer 12

1/s * e^(as)^2 * erf(as)
a >= 0

Question 13

L{f(at)}

Answer 13

1/a * F(s/a)
a > 0

Question 14

L{f(t-a) * u(t-a)}

Answer 14

e^(-as) F(s)

Question 15

L{e^(-at) * f(t)}

Answer 15

F(s + a)

Question 16

L{g^(n) of (t)}

Answer 16

s^n * G(s) - s^(n-1) g(0) - s^(n-2) g’(0) - … - g^(n-1)(0)

Question 17

L{(f*g)(t)}

Answer 17

F(s) * G(s)

Question 18

L{ t * f(t) }

Answer 18

-F’(s)

Question 19

L{ t^n * f(t) }

Answer 19

(-1)^n * (nth derivative)F(s)

Question 20

L{ int[0, x]: f(t) dt }

Answer 20

1/s * F(s)