[clug-progsig] 41%

[Aaron Rustad]

Hi Michael, 

I am just wondering why you chose C as the language to learn in order
solve these equations.

AR.


On Mon, 21 Feb 2005 22:54:05 -0700, Michael Walters
<waltersm at telusplanet.net> wrote:
> Hello Shawn Grover and others on the list,
> 
> I am now about 41% the way through the absolute beginner's guide to c, and the
> last four chapters went very quickly as I saw the ways that I did certain
> things in Fortran and Assembler are easily done in c, such as incrementing
> and decrementing registers, with the added feature of post incrementing
> versus pre incrementing and post decrementing versus pre decrementing
> counters.
> 
> The things that were done in the text brought back memories of my computer
> course at SAIT between 1970 and 1976 with two years off in the middle to pay
> off the student loan, and the extra two years I took repeating failed courses
> due to relapses of my schizophrenia.
> 
> My previous knowledge from my computer courses enabled me to absorb some of
> the concepts a little faster than someone who had never graduated from a two
> year computer program.
> 
> At the rate I am now going I should complete the "absolute beginner's guide to
> c" in about 10 more days.
> 
> Then I have the other 13 c books and three c++ books to study.
> 
> In the not too distant future I expect to be able to write a c program to
> solve exp(x +jy) = x + jy where j = square root of -1.
> 
> Even if C does not have complex number functions, I could still do the complex
> number calculations using the rules of complex multiplication, division,
> addition, subtraction, and exponentiation using real number operations.
> 
> For example, exp(x + jy) = exp(x)*cos(y) + j*exp(x)*sin(y).
> And (x1 + jy1)*(x2 + jy2) = (x1*x2 - y1*y2) + j*(x1*y2 + x2*y1)
> 
> et cetera.
> 
> All solutions of exp(x + jy) = x + jy come in complex conjugate pairs, a thing
> which I discovered myself, but which someone who had taken advanced analysis
> says is true of all analytic functions f(x + jy). That is the solutions to
> any equation of the form f(x + jy) = x + jy occur in complex conjugate pairs
> if f is analytic.
> 
> I was able to find three complex conjugate pairs of solutions to exp(x + jy) =
> x + jy, but I misplaced the solutions and the programmable calculators on
> which I did them are worn out. Unfortunately I have not replaced those
> calculators.
> 
> However, when I learn the transcendental functions sin(x), cos(x), tan(x),
> exp(x) in c, I should be able to solve those equations and perhaps find more
> complex conjugate pairs of solutions.
> 
> I was able to prove that there are infinitely many solutions to exp(x + jy) =
> x +jy, but of course, with round off errors we can only find a find a finite
> number of those solutions.
> 
> Anyone who has successfully passed first year calculus can prove that exp(x) =
> x has no solution in the real number field. But there are infinitely many
> complex conjugate pairs of solutions in the complex field.
> 
> I expect to be able to start solving those equations using numerical methods
> and c in perhaps a couple of months.
> 
> Regards,
> 
> Michael Walters - clug two tier member and member of the programming special
> interest group.
> 
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