Skip to content

Commit 3c68c06

Browse files
SchrausserSchrausser
authored
Create README.html
1 parent bca65a6 commit 3c68c06

File tree

1 file changed

+132
-0
lines changed

1 file changed

+132
-0
lines changed

‎README.html‎

Lines changed: 132 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,132 @@
1+
<html>
2+
<head>
3+
<meta charset="utf-8">
4+
<meta name="viewport" content="width=device-width, initial-scale=1.0">
5+
<meta name="Author" content="Dietmar Gerald Schrausser">
6+
7+
<title>
8+
ConsoleApp_Integral/README
9+
</title>
10+
11+
</head>
12+
<body style="font-family:calibri;font-size:85%;background-color:#eceff1;color:#37474f">
13+
14+
<style>
15+
a {color: #78909c; }
16+
a:visited {color: #78909c;}
17+
</style>
18+
<h1 id="consoleapp_integral">ConsoleApp_Integral</h1>
19+
<p>Console applications for <em>integral</em> and <em>interpolation</em> (German).</p>
20+
<h2 id="romi">ROMI</h2>
21+
<p>Approximiert (a) Flächen- oder (b) Kurven-Integrale</p>
22+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><munderover><mo data-mjx-texclass="OP">&int;</mo><mi>a</mi><mi>b</mi></munderover><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>d</mi><mi>x</mi></math></p>
23+
<p>mittels Romberg Methode, dabei
24+
ggf. Dateiausgabe nach <code>romi.txt</code> von Funkionsmatrix</p>
25+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">y</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow><mo>,</mo></math></p>
26+
<p>bei</p>
27+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>d</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><munderover><mo data-mjx-texclass="OP">&int;</mo><mi>a</mi><mi>b</mi></munderover><mrow data-mjx-texclass="ORD"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>d</mi><mi>x</mi></mrow><mo>.</mo></math></p>
28+
<ul>
29+
<li>Ausführung von <code>ROMI.bat</code>:</li>
30+
<li>Definition von <math display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> in <code>ROMI.h</code>;</li>
31+
<li>Compilieren von <code>ROMI.c</code>;</li>
32+
<li>Ausführung von <code>ROMI.exe</code>.</li>
33+
</ul>
34+
<p>Handhabung</p>
35+
<pre><code>ROMI [a] [b] [d] [m] [F]
36+
[a] ..... Integrations Minimum a
37+
[b] ......Integrations Maximum b
38+
[d] ......Delta d
39+
[m] ......Modus: (0)Flaechen.I (1)Kurven.I
40+
[F] ......Funktionsmatrix: (0)keine (1)romi.txt
41+
</code></pre>
42+
<h2 id="rome">ROME</h2>
43+
<p>Approximiert das Integral <math display="inline"><munderover><mo data-mjx-texclass="OP">&int;</mo><mi>a</mi><mi>b</mi></munderover><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>d</mi><mi>x</mi></math>
44+
mittels <em>Romberg-Extrapolation</em>
45+
(ROMBERG Integration nach Meyberg und Vachenauer, <a href="https://doi.org/10.1007/978-3-642-56654-7_4">2001</a>, S. 209).</p>
46+
<ul>
47+
<li>Ausführung von <code>ROME.bat</code>:</li>
48+
<li>Definition von <math display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> in <code>ROME.h</code>;</li>
49+
<li>Compilieren von <code>ROME.c</code>;</li>
50+
<li>Ausführung von <code>ROME.exe</code>.</li>
51+
</ul>
52+
<p>Handhabung</p>
53+
<pre><code>ROME [a] [b]
54+
[a] ....... Integrations Minimum a
55+
[b] ....... Integrations Maximum b
56+
</code></pre>
57+
<h2 id="kusi">KUSI</h2>
58+
<p>Kubische Spline Interpolation: Berechnung der Koeffizientenmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">A</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">b</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">c</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">d</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> sowie <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">s</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> zu einer (empirischen) Funktionsmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">y</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math>, wobei</p>
59+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>s</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>y</mi><mi>i</mi></msub><mo>+</mo><msub><mi>b</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><msub><mi>x</mi><mi>i</mi></msub><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><msub><mi>d</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><msub><mi>x</mi><mi>i</mi></msub><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mo>;</mo><mi>i</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>n</mi><mo>&minus;</mo><mn>1.</mn></math></p>
60+
<ul>
61+
<li>Übernahme einer ASCII Funktionsmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi></mrow></math>;</li>
62+
<li>Ausgabe der ASCII Koeffizientenmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">A</mi></mrow></math> (<code>KUSI.txt</code>);</li>
63+
<li>Berechnung von <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">s</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> über die Interpolations-Funktion.</li>
64+
</ul>
65+
<p>Handhabung</p>
66+
<pre><code>KUSI [f] [x]
67+
[f] ......... Funktionsmatrix Datei (F)
68+
[x] ......... Funktionswert x
69+
</code></pre>
70+
<h2 id="kusf">KUSF</h2>
71+
<p>Kubische Spline Funktion: Berechnung einer Funktionsmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">p</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> zu Koeffizientenmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">A</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">b</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">c</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">d</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math>, wobei</p>
72+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>s</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>y</mi><mi>i</mi></msub><mo>+</mo><msub><mi>b</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><msub><mi>x</mi><mi>i</mi></msub><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><msub><mi>d</mi><mi>i</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><msub><mi>x</mi><mi>i</mi></msub><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mo>;</mo><mi>i</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>n</mi><mo>&minus;</mo><mn>1.</mn></math></p>
73+
<ul>
74+
<li>Übernahme einer ASCII Funktionsmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi></mrow></math>;</li>
75+
<li>Übernahme der ASCII Koeffizientenmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">A</mi></mrow></math> (<code>KUSI.txt</code>);</li>
76+
<li>Ausgabe der ASCII Funktionsmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">S</mi></mrow></math> (<code>KUSF.txt</code>).</li>
77+
</ul>
78+
<p>Handhabung</p>
79+
<pre><code>KUSF [f] [a] [b] [d]
80+
[f] ......... Funktionsmatrix Datei (F)
81+
[a] ......... (x) Minimum
82+
[b] ......... (x) Maximum
83+
[d] ......... Intervall d
84+
</code></pre>
85+
<h2 id="nwti">NWTI</h2>
86+
<p>Newton Interpolation: Berechnung des Koeffizientenvektors <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">a</mi></mrow></math> sowie <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">p</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> zu einer (empirischen) Funktionsmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">y</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math>, wobei</p>
87+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>.</mo><mo>.</mo><mo>.</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mi>n</mi><mo stretchy="false">)</mo><mo>.</mo></math></p>
88+
<ul>
89+
<li>Übernahme einer ASCII Funktionsmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi></mrow></math>;</li>
90+
<li>Ausgabe einer ASCII Koeffizientenvektor Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">a</mi></mrow></math> (<code>nwti.txt</code>);</li>
91+
<li>Berechnung von <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">p</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> über das Interpolations-Polynom.</li>
92+
</ul>
93+
<p>Handhabung</p>
94+
<pre><code>NWTI [f] [x]
95+
[f] ......... Funktionsmatrix Datei (F)
96+
[x] ......... Funktionswert x
97+
</code></pre>
98+
<h2 id="nwtp">NWTP</h2>
99+
<p>Newton Interpolations Polynom: Berechnung einer Funktionsmatrix <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi><mo mathvariant="bold-italic">=</mo><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mrow data-mjx-texclass="ORD"><mo mathvariant="bold-italic" stretchy="false">|</mo></mrow><mi mathvariant="bold-italic">p</mi><mo mathvariant="bold-italic" stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold-italic" stretchy="false">)</mo><mo mathvariant="bold-italic" stretchy="false">)</mo></mrow></math> zu Koeffizientenvektor <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">a</mi></mrow></math>, wobei</p>
100+
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>.</mo><mo>.</mo><mo>.</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>&middot;</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>&middot;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&minus;</mo><mi>n</mi><mo stretchy="false">)</mo><mo>.</mo></math></p>
101+
<ul>
102+
<li>Übernahme der ASCII Koeffizientenvektor Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">a</mi></mrow></math> (<code>nwti.txt</code>);</li>
103+
<li>Ausgabe der ASCII Funktionsmatrix Datei <math display="inline"><mrow data-mjx-texclass="ORD"><mi mathvariant="bold-italic">F</mi></mrow></math> (<code>nwtp.txt</code>).</li>
104+
</ul>
105+
<p>Handhabung</p>
106+
<pre><code>NWTP [a] [b] [d]
107+
[a] ......... (x) Minimum
108+
[b] ......... (x) Maximum
109+
[d] ......... Intervall d
110+
</code></pre>
111+
<br>
112+
<h2 id="references">References</h2>
113+
<p>Meyberg, K., &amp; Vachenauer, P. (2001). Integration. In <em>Höhere Mathematik 1</em>. Springer-Lehrbuch. Springer, Berlin, Heidelberg. <a href="https://doi.org/10.1007/978-3-642-56654-7_4">https://doi.org/10.1007/978-3-642-56654-7_4</a></p>
114+
115+
<hr WIDTH="75%">
116+
<blockquote ALIGN="CENTER">
117+
<center>
118+
<a href="https://github.com/Schrausser/ConsoleApp_Integral">
119+
ConsoleApp_Integral
120+
</a>
121+
<br><font color="#999999"><font size=-1>
122+
<a
123+
href="https://orcid.org/0000-0002-4924-8280">
124+
Dietmar Gerald Schrausser
125+
</a>
126+
<p>22.07.2025</p>
127+
</font></font>
128+
</center>
129+
</blockquote>
130+
131+
</body>
132+
</html>

0 commit comments

Comments
 (0)