"Kreyszig" Laplace Transforms for LETS and USURY
     JCT: In "Advanced Engineering Mathematics" by Erwin Kreyszig, 
both the "LETSystem account equation" and the "Usury system account 
equation" are on the same page. (Page 148 Chapter 4, Laplace 
Transformations, Example #1 and Example #2). 
     I will denote an integral from 0 to infinity(oo) of the function 
f(t) by 0/oo {f(t)}. e is the base 2.71 for natural exponentiating.
     In Basic language, * is multiplication and ^ is exponentiation. 
     From page 148: 
"The Laplace Transformation of a function will be denoted by L [f(t)]. 
Hence, F(s) = L [f(t)] = 0/oo {f(t)*(e^(-st))*dt}. 
The described operation on f(t) is called the Laplace Transformation. 
We shall denote the original function by a lower case letter and its 
transform by the same letter in Capital. 
Example 1. 
Let f(t) = 1 when t > 0. Then:
L [f(t)] = L [1] = 0/oo {1*(e^(-st))*dt} = -e^(-st)/s from 0 to oo;
Hence, when s > 0, L [1] = 1/s 
Example 2. 
Let f(t) = e^(it) when t > 0 where i is a constant. Then 
L [f(t)] = L [e^(it)] = 0/oo {(e^(it))*(e^(-st))*dt} 
= e^(-(s-i)t)/(i-s) from 0 to oo; 
Hence, when s-i > 0, L [e^(it)] = 1/(s-i). 
     JCT: The first equation represents a stable LETS account (1/s). 
The second equation represents a positive feedback which generates 
exponential growth, the equation of a usury currency account 1/(s-i).
     It is interesting to note that the first two examples of the very 
simplest Laplace Transformations in his book are the linear LETS 
accounts and exponential usury accounts. 
     It is also interesting to note that the only difference between 
the two is that in a LETS banking system, i=0 so that there is no 
positive feedback on debt. This obeys all the religious prohibitions 
against exacting interest. 
"Kreyszig" Laplace Transforms of LETS & Usury #2
>Date: Thu Jun  3 22:52:41 1999
>From: william_b_ryan@hotmail.com ("William B.Ryan")
>Subject: Re: [lets] Laplace Transforms of LETS & Usury
>Posted to several lists May 24, John Turmel wrote:
>>In "Advanced Engineering Mathematics" by Erwin Kreyszig, both the
>>"LETSystem account equation" and the "Usury system account equation
>>are on the same page. (Page 148 Chapter 4, Laplace Transformations,
>>Example #1 and Example #2).
>Since reading this, I have consulted several editions of Kreyszig's
>book. In none of them, repeat--none of them--are mentioned the
>words "LETS" or "usury." Not on page 148 or anywhere.
     JCT: They may not be mentioned but Example equation #1 is the 
LETS equation and Example equation #2 is the equation of a bank 
account. All you have to do is convert the Laplace Transforms to their 
control systems to see it. 
>There IS a chapter 5 entitled "Laplace Transformations." There are
>examples 1 and 2 at page 201 in most editions. Turmel's examples
>appear to be mangled transliterations of Kreyszig's examples, being
>the derivations of Laplace Transforms for simple linear and
>exponential functions.
     JCT: I don't know what's mangled about it. The LETS equation 
(1/s) is the simple linear function and the USURY equation (1/(s-i) is 
the exponential function. What's hard? 
>I say mangled because it is difficult to follow Turmel's 
>transliterations, but also because there are definite alterations.
     JCT: How would you transliterate it? It's not easy explaining 
exponentials with their use of superscripts in ASCII. So I used Basic 
Language programming. Seems to me you don't recognize Basic 
Programming Language, something most computer programmers learn from 
the very start. 
>For instance, Turmel uses the letter "i" to imply interest in his
>example 2, where Kreyszig uses the italicized "a."
     JCT: Sure I could have used "a" and said "Let a=interest rate." 
Instead I used "i" for interest rate. So I used a different label. 
What a trite objection. 
>I think this says a lot about Turmel's intellectual integrity.
     JCT: This is silly. It's like a teacher who happens to be using a 
textbook which solves for "a" when the equation is a+2=4 to find the 
answer a=2 is somehow derelict if he solves for x+2=4 instead of 
a+2=4. The techniques are identically valid and only the name of the 
variable is different. It would be just as silly to impugn his 
intellectually integrity as it is to impugn mine for doing the example 
using "i" instead of "a" when all I'd have had to do is say "let 
a=interest rate" instead of "i=interest rate." 
>This is a man who calls himself an "engineer" when he is definitely
>NOT an engineer.
     JCT: Wes Burt, you're an engineer. Was my use of a different 
letter to teach the Laplace Transform technique in any way fraudulent 
or did it in any way change Kreyszig's meaning? 
     This is such an inane objection that it really does raise 
questions as to Bill's mathematical qualifications, doesn't it? 
>This is a man who "decodes" "differential equations" but not
>"Laplace Transforms" in the Biblical words of Jesus.
     JCT: Of course, since Christ's words "To those who have 
abundance will more be given and from those who have no abundance, 
even what they have will be taken away" to boil down to the 
differential equation dB/dt=aB, that can then be converted to the 
Laplace Transform 1/(s-a). So you could say that we can detect a 
Laplace Transform in those words even if Bill doesn't see it. 
>This is a man who calls bankers and other persons who he terms
>"sheeple" or "positives," "sinners," while he himself admittedly 
>earns his living as a professional gambler, a "profession" that 
>arguably contributes nothing to society except heartache and despair.
>If there is such a thing as social parasites, I think gamblers must 
>be somewhere near the top of the list of those who would qualify to 
>be placed within that classification.Bill Ryan
     JCT: And the millions I've earned as a professional gambler have 
almost all been spent in trying to free the poor from their debts with 
LETS. I think I'll be forgiven but I don't think the bankers will. 
     Of course, now Bill's trying to argue that what I have do say has  
no merit because of what I do, a cheap debate ploy. 
     So Bill's not a professional gambler. You have to realize that 
gambling at games of skill is constantly using your brain which 
explains why I'm so sharp and Bill's so dull. He sounds like a sore 
loser quibbling over trivial objections. 
     When it comes to fraudulent performance, I'd point out that 
you're the guy who told us there are expanding nodalities which is 
false. And you're the guy who said there are front-end mortgages where 
the banker lends you not only the principal but also the interest 
which also seems false. I haven't had to use one false claim in my 
arguments but you have. So whose integrity is really on the line? 
>Date: Fri Jun  4 00:01:42 1999
>From: charliecmt@hotmail.com (Charles Michael)
>Subject: [lets] TIME OUT!!!
>Okay guys, maybe it is time to end the debate. Clearly both debaters 
>(John & Bill) are "true believers" who are not going to be disuaded 
>from their own view of things.
     JCT: Not on your life would I end the debate with you thinking 
that maybe Bill made sense. As far as I'm concerned, this aspersion on 
my scientific integrity because I used a different letter in my 
equation is so silly that it once again casts doubt on his technical 
>IMHO the debate no longer serves a purpose when a part of every post
>involves needling, disparaging and name calling which has occurred on 
>both sides to some degree.
     JCT: I will not allow anyone to leave the debate thinking Bill 
might have been right. I'll beat up his brain as long as he wants to 
keep coming up with his ridiculous statements. The more he keeps 
posting foolish argument, the more likely people will stop taking him 
>Can we just cool it and move onto other topics please?
     JCT: Don't worry about the needling, disparaging and name 
calling. It actually makes the debate more entertaining for the 
readers. And besides, when my opponent starts foaming at the mouth, I 
am sure it's because he's losing the debate. Remember that his view of 
things is wrong as I've been able to show over and over again.  
     But if Wes Burt tells me he agrees that my using "i" instead of 
"a" in explaining the technique is in someway fraudulent, then I'll 
apologize and change it to "a" on my web site and say that 
"a=interest" instead of "i=interest." 
"Kreyszig" Laplace Transforms of LETS & Usury #3
>From: william_b_ryan@hotmail.com
>Date: Fri Jun  4 19:39:36 1999
>The deception is putting quotation marks around "LETSystem account
>equation" and "Usury system account equation" thereby implying they 
>are quotations from Kreyszig.
     JCT: If you so choose to interpret it that way, there's nothing I 
can do but I think it's pretty clear that the quotation marks around 
"LETSystem account equation" and "Usury system account equation" are 
in introduction to the Kreyszig text preceded by JCT:. It is a totally 
unfair allegation to say words I've highlighted in my intro are meant 
to imply that they are quotations from Kreyszig. I have faithfully 
reproduced the text from his book other than the one instance where 
rather than saying "a = interest rate," I used "i" for interest as 
I've always done. Had I left example 2 with "a" as my variable, and 
then mentioned that "a" is interest. I'm not going to make it harder 
to understand just to suit your taste.
     Besides, Kreyszig was written in the early 1970s and LETS started 
in the mid 1980s so anyone familiar with LETS cannot not come to same 
conclusion you want to come to. And do you really think you'd find the 
word "usury" in a math book when 99% of people, including most 
mathematicians and even Socreds, not including Quebec Socreds, have no 
idea what usury really means?  
>It is also deceptive to change Kreyszig's italicized "a" into "i."
     JCT: I'm amazed that you keep keep repeating this silly 
objection. It's a complaint about form and not substance. Just like 
your complaint that I used Basic language to handle the equations. 
Purely a question of form. Never substance. If this is the best that 
you can do, sure, replace "a" instead of "i" and now tell me what's 
wrong with my explanation of the Laplace Transform technique. But if 
you don't like Basic, how would you have written the equations for 
presentation to an ASCII audience? 
>And why even "reference" Kreyszig's text or any other engineering 
>text at all, except to lend credence to your bogus claim to being an
     JCT: I'm don't think too many people aren't convinced that I'm a 
qualified engineer. Didn't I know that your nodality theory violated 
Kirchoff's Law? As Wes pointed out, it's not something that the 
average layman learns and it's obvious you never learned it at all. 
>or to lend credence to your assertion that LETS has anything to do 
>with engineering, 
     JCT: I think that is has optimum money system engineering design 
and the advanced engineering mathematical analysis I've provided to 
prove that point has never been challenged, not even by you. Sure you 
call LETS a crank theory but all the people using the working models 
would be hard pressed to agree with you. 
>or to falsely imply Kreyszig endorses LETS?  
     JCT: I was quite careful to only quote Kreyszig in the 
development of the technique and quite careful to label with JCT: my 
use of that technique to explain LETS. You choose to see it in the 
most malevolent way possible but you have to first ignore that the 
LETS wasn't even in existence when the book was written. 
>And what do Laplace Transforms have to do with the theoretical
>concepts we are discussing, except bringing smoke and mirrors into
>the discussion? 
     JCT: You brought your differential equations to the theoretical 
concepts you were discussing, I brought the superior Laplace 
Transformations to the real-world engineering I was discussing. Any 
engineer could explain how Laplace Transformations handle the same 
problems as do differential equations but in a much simple more 
sophisticated fashion. It's why I've kept catching your mathematical 
mistakes and you've found no substantive errors in mine. So far, your 
only quasi-valid complaint is an irrelevant change in labelling my 
variable to make it easier to understand. 
     Besides, if you looked at the control system in the bankmath.htm, 
you'd realize what Laplace Transformations have to do with what we are 
discussing. You can't draw the control system of the bank accounts 
with your differential equations but Laplace Transforms provide the 
easiest way to draw their control systems for a blueprint view of 
these concepts. 
>We are not doing actual calculations, which in some applications may 
>indeed be simplified by Laplace Transforms, but developing concepts, 
>which are best conveyed through calculus.
     JCT: You don't want to do the calculations and you've never 
responded when we asked you to but I sure am doing actual 
calculations. We are calculating the debt versus the money we have to 
pay it with. 
     I can't accept that any ideas are better conveyed through the 
more difficult than the more easy to understand Laplace 
Transformations. Laplace Transformations reduces calculus problems to 
algebraic manipulations which is far simpler than having to do it with 
integration or differentiation. As long as you keep insisting that  
doing it the hard way is better than doing it the easy way, I'll keep 
catching you in the mathematical errors you keep making. And to which 
you have never responded. You never answered when I caught your 
errors. I repointed them all out again in submission #16. Would you 
like me to point them out again?
>You are quite apparently trying to impress people with your "superior"
     JCT: No, I'm trying to shut up people with inferior knowledge but 
it doesn't seem to be working in your case. You've been wrong all the 
way, Bill, and no amount of name calling is going to change the fact 
that you've backed down from every one of my challenges to your 

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