diff options
author | Thomas Albers Raviola <thomas@thomaslabs.org> | 2024-05-21 11:32:09 +0200 |
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committer | Thomas Albers Raviola <thomas@thomaslabs.org> | 2024-05-21 11:32:09 +0200 |
commit | 6fb1cd644308ac46a71536cc7da3a16377107b4f (patch) | |
tree | 4aa8f904ced791c3b3076d78525636ef0312e6d3 /t | |
parent | f19998f7fd9db2bd1ed4eb80ea1744a013b166fa (diff) |
Diffstat (limited to 't')
-rw-r--r-- | t/test1.chn | 14 | ||||
-rw-r--r-- | t/test2.chn | 19 | ||||
-rw-r--r-- | t/test3.chn | 9 | ||||
-rw-r--r-- | t/test4.chn | 65 |
4 files changed, 0 insertions, 107 deletions
diff --git a/t/test1.chn b/t/test1.chn deleted file mode 100644 index f55fb70..0000000 --- a/t/test1.chn +++ /dev/null @@ -1,14 +0,0 @@ -{@define}{@author}{Thomas Albers Raviola}% -{@define}{@today}{May 12, 2024}% -{@define}{@printdate}{{@lambda}{@date}{the date is @date}}% -{@section}{Introduction} - -Hello, this is a sample of a program written in chains - -Chains was created by @author to help him write articles of questionable -usefulness. - -{@printdate}{@today} -{@section}[Conclusion] - -idk man, guess it works, don't it? diff --git a/t/test2.chn b/t/test2.chn deleted file mode 100644 index a637b61..0000000 --- a/t/test2.chn +++ /dev/null @@ -1,19 +0,0 @@ -{@define}{@html-element}{{@lambda}{@name}{{@lambda}{@attr @content}{<@name @attr> -@content -</@name>}}}% -% -% -{@define}{@html-html}{{@html-element}{html}}% -{@define}{@html-head}{{@html-element}{head}}% -{@define}{@html-body}{{@html-element}{body}}% -{@define}{@html-title}{{@html-element}{title}}% -{@define}{@html-h1}{{@html-element}{h1}}% -{@define}{@html-p}{{@html-element}{p}}% -% -% -{@html-html}{}{% -{@html-head}{}{{@html-title}{}{Website}}% - -{@html-body}{}{ -{@html-h1}{}{Chains test} -{@html-p}{}{Hello World!}}} diff --git a/t/test3.chn b/t/test3.chn deleted file mode 100644 index 2fbdeab..0000000 --- a/t/test3.chn +++ /dev/null @@ -1,9 +0,0 @@ -@define{@define-function}{@syntax{@name @args @body}{@define{@name}{@lambda{@args}{@body}}}}% -@define-function{@foo}{@a @b}{hola @b}% -@foo{mundo}{casa} -@define{@section}{@lambda*{@title}{@gp{@quote{@section}}}{@title@siblings@title -}}% -@section{Hello World} -hola -@section{Good Bye World} -chao diff --git a/t/test4.chn b/t/test4.chn deleted file mode 100644 index e126091..0000000 --- a/t/test4.chn +++ /dev/null @@ -1,65 +0,0 @@ -{@define}{@title}{Method for solving first order and Bernoulli's differential equations} -{@define}{@author}{Thomas Albers Raviola} -{@define}{@date}{2022-10-01} -% -{@template} -{@section}{History} -I came across the method concerning this article in an old math book from Doctor -Granville (Elements of differential and integral calculus - ISBN-13: -978-968-18-1178-5). It doesn't appear to be a popular technique as when using it -for my assignments I always had to explain what I was doing. As of yet, I still -haven't found another text referencing it, which is why I decided to include it -in my website. - -In the original book this procedure is shown but never really explained, it is -left as a sort of "it just works" thing. Here is my attempt to it clear. - -{@section}{Theory} -Throughout this article we'll consider first order differential equations with -function coefficients just as a special case of the Bernoulli's differential -equation with {@eq*}{n = 0}. - -Consider now the following ODE: -{@equation}{ -y' + P(x)y = Q(x)y^n -} - -let {@eq*}{y} be the product of two arbitrary functions {@eq*}{w} and {@eq*}{z} -such that - -{@equation}{ -y &= wz \\ -y' &= w'z + wz' -} - -we now restrict {@eq*}{z} to be the solution of the ODE - -{@equation}{ -z' + P(x)z = 0 -} - -with this it is possible to solve for {@eq*}{z} by integrating - -{@equation}{ -\frac{z'}{z} = - P(x) -} - -using {@eq}{z} we solve for {@eq}{w} by replacing {@eq}{y} inside the original -ODE - -{@align}{ -w'z + wz' + P(x)wz &= Q(x)w^nz^n \\ -w'z + w\left(z' + P(x)z\right) &= Q(x)w^nz^n \\ -w'z &= Q(x)w^nz^n \\ -\frac{w'}{w^n} &= Q(x)z^{n-1} -} - -the general solution to our original ODE can be simply obtained by multiplying -{@eq*}{w} and {@eq*}{z}. - -{@section}{Comments} -This method, while functional, may not always be the most practical. In some -cases the differential equations for $w$ and $z$ may not have closed algebraic -solutions. A more traditional substitution may in some situations also be easier -than this method. Like always it is up to one to know which tool to apply for a -given problem. |