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I can appreciate you gentlemen (and I use that term loosely) making conclusory statements that 2+2 should always equal 4, but there have to be instances where the equation can equal something other than 4...I don't buy the simple explanation as you were taught in 2nd grade. Polls are not appropriate because you need to show your work...where the heck is OCinBuffalo or DCTom?? I want to see a proof.

Posted

I can appreciate you gentlemen (and I use that term loosely) making conclusory statements that 2+2 should always equal 4, but there have to be instances where the equation can equal something other than 4...I don't buy the simple explanation as you were taught in 2nd grade. Polls are not appropriate because you need to show your work...where the heck is OCinBuffalo or DCTom?? I want to see a proof.

racist.
Posted

. . . I want to see a proof.

http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf

 

f (t)=L-1 F(s) F(s)=L f (t) f (t)=L-1 F(s) F(s)=L f (t) {}{}{}{}

1.1

3. tn, 5. t

1 2.eat

s s-a

1

G(p+1) sp+1

n=1,2,3,K

n! 4. tp ,p>-1 sn+1

p 6. tn-12, n=1,2,3,K 22

1×3×5L(2n-1) p

2s3

a 8.

tsin(at) 2 10. (s2 +a2)

2a3 sin(at)-atcos(at) 2 12.

2n sn+1 s

7. sin(at)

s2 +a2 2as

cos(at)

tcos(at) 2

9.

11.

13.

15. 17. 19.

21. 23.

25.

27. 29.

31.

33.

35. 37.

s2 +a2 s2 -a2

(s2 +a2)

(s2 +a2)

2as2 sin(at)+atcos(at) 2

(s2 +a2)

s(s2 -a2) cos(at)-atsin(at) 2 14.

s(s2 +3a2) cos(at)+atsin(at) 2

(s2 +a2) sin(at+b) ssin(b)+acos(b) 16.

(s2 +a2) scos(b)-asin(b)

s2 +a2

sinh(at) a 18.

cos(at+b)

cosh(at) s

eat sin(bt) eat sinh (bt )

tneat, n=1,2,3,K u (t)=u(t-c)

b s-a 2 20. eat cos(bt) 2

s2 -a2

s2 +a2 s2 -a2

(s-a) +b2 (s-a) +b2 b s-a

22.

24.

F(s) ts0s

eat cosh (bt ) f (ct )

2 (s-a) -b2

n! (s-a)n+1

2 (s-a) -b2

1 Êsˆ c F Á c ̃

26.

u (t)f (t-c) e-csF(s) 28. u (t)g(t)

c

e-cs s

d (t - c)

Dirac Delta Function

Ë ̄ e-cs

Heaviside Function

cc

ectf(t) F(s-c) 30. tnf(t), n=1,2,3,K

e-csL{g(t+c)}

(-1)nF(n)(s)

1 f (t) Ú• F(u)du 32. Út f (v)dv

Út

0 f (t-t)g(t)dt

f¢(t) f(n)(t)

F(s)G(s) sF(s)- f (0)

34. f (t+T)= f (t) 36. f¢(t)

ÚT e-st f (t)dt 0

1-e-sT s2F(s)-sf (0)- f¢(0)

snF(s)-sn-1 f (0)-sn-2 f¢(0)L-sf(n-2)(0)- f(n-1)(0)

Table Notes

1. This list is not a complete listing of Laplace transforms and only contains some of the more commonly used Laplace transforms and formulas.

2. Recall the definition of hyperbolic functions.

et +e-t et -e-t cosh(t)= 2 sinh(t)= 2

3. Be careful when using “normal” trig function vs. hyperbolic functions. The only difference in the formulas is the “+ a2” for the “normal” trig functions becomes a “- a2” for the hyperbolic functions!

4. Formula #4 uses the Gamma function which is defined as

G(t)=Ú•e-xxt-1 dx 0

If n is a positive integer then,

G(n+1)= n!

The Gamma function is an extension of the normal factorial function. Here are a couple of quick facts for the Gamma function

G(p+1)= pG(p) p(p+1)(p+2)L(p+n-1)= G(p+n)

G(p) GÊ1ˆ= p

Á ̃ Ë2 ̄

 

therefore, 2+2=4

Posted

I can appreciate you gentlemen (and I use that term loosely) making conclusory statements that 2+2 should always equal 4, but there have to be instances where the equation can equal something other than 4...I don't buy the simple explanation as you were taught in 2nd grade. Polls are not appropriate because you need to show your work...where the heck is OCinBuffalo or DCTom?? I want to see a proof.

 

!@#$ing lawyers.

Posted

I don't know about 2 + 2, but I did have a professor in Engineering school provide proof that women are evil. It was derived like this:

 

I think we'd all agree that being with a women is a product of time and money (vis-a-vis, nobody that is too broke or too busy can court a women), therefore:

 

Women = Time x Money

 

And as we all know, Time IS Money, therefore:

 

Women = Money x Money = (Money)^2

 

I'm sure you've all heard that "Money is the root of evil", therefore (If Money = [Evil]^[1/2]):

 

Women = ([Evil]^[1/2])^2

 

Women = Evil

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