Jump to navigation Jump to search

General

Display information for equation id:math.240524.0 on revision:240524

* Page found: Volume element (eq math.240524.0)

(force rerendering)

Occurrences on the following pages:

Hash: d39553232cff16d1f06090f4c202effd

TeX (original user input):

dV = \rho(u_1,u_2,u_3)\,du_1\,du_2\,du_3

TeX (checked):

dV=\rho (u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}

LaTeXML (experimental; uses MathML) rendering

MathML (6.536 KB / 1.041 KB) :

d V = ρ ( u 1 , u 2 , u 3 ) d u 1 d u 2 d u 3 𝑑 𝑉 𝜌 subscript 𝑢 1 subscript 𝑢 2 subscript 𝑢 3 𝑑 subscript 𝑢 1 𝑑 subscript 𝑢 2 𝑑 subscript 𝑢 3 {\displaystyle dV=\rho(u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle dV=\rho(u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
      <mrow id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">d</mi>
        <mo id="p1.1.m1.1.27.1.1" xref="p1.1.m1.1.27.1.1.cmml"></mo>
        <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">V</mi>
      </mrow>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mrow id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml">
        <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ρ</mi>
        <mo id="p1.1.m1.1.27.2.1" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.27.2.2" xref="p1.1.m1.1.27.2.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.27.2.2.1.cmml">(</mo>
          <msub id="p1.1.m1.1.27.2.2.2" xref="p1.1.m1.1.27.2.2.2.cmml">
            <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">u</mi>
            <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">1</mn>
          </msub>
          <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.27.2.2.1.cmml">,</mo>
          <msub id="p1.1.m1.1.27.2.2.3" xref="p1.1.m1.1.27.2.2.3.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">u</mi>
            <mn id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">2</mn>
          </msub>
          <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.27.2.2.1.cmml">,</mo>
          <msub id="p1.1.m1.1.27.2.2.4" xref="p1.1.m1.1.27.2.2.4.cmml">
            <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">u</mi>
            <mn id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">3</mn>
          </msub>
          <mo rspace="4.2pt" stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.27.2.2.1.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.27.2.1a" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">d</mi>
        <mo id="p1.1.m1.1.27.2.1b" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mpadded width="+1.7pt" id="p1.1.m1.1.27.2.3" xref="p1.1.m1.1.27.2.3.cmml">
          <msub id="p1.1.m1.1.27.2.3a" xref="p1.1.m1.1.27.2.3.cmml">
            <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">u</mi>
            <mn id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">1</mn>
          </msub>
        </mpadded>
        <mo id="p1.1.m1.1.27.2.1c" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">d</mi>
        <mo id="p1.1.m1.1.27.2.1d" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mpadded width="+1.7pt" id="p1.1.m1.1.27.2.4" xref="p1.1.m1.1.27.2.4.cmml">
          <msub id="p1.1.m1.1.27.2.4a" xref="p1.1.m1.1.27.2.4.cmml">
            <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">u</mi>
            <mn id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">2</mn>
          </msub>
        </mpadded>
        <mo id="p1.1.m1.1.27.2.1e" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">d</mi>
        <mo id="p1.1.m1.1.27.2.1f" xref="p1.1.m1.1.27.2.1.cmml"></mo>
        <msub id="p1.1.m1.1.27.2.5" xref="p1.1.m1.1.27.2.5.cmml">
          <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">u</mi>
          <mn id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">3</mn>
        </msub>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
        <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
        <apply id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">
          <times id="p1.1.m1.1.27.1.1.cmml" xref="p1.1.m1.1.27.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑑</ci>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑉</ci>
        </apply>
        <apply id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">
          <times id="p1.1.m1.1.27.2.1.cmml" xref="p1.1.m1.1.27.2.1"/>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝜌</ci>
          <vector id="p1.1.m1.1.27.2.2.1.cmml" xref="p1.1.m1.1.27.2.2">
            <apply id="p1.1.m1.1.27.2.2.2.cmml" xref="p1.1.m1.1.27.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.2.2.1.cmml" xref="p1.1.m1.1.27.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑢</ci>
              <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">1</cn>
            </apply>
            <apply id="p1.1.m1.1.27.2.2.3.cmml" xref="p1.1.m1.1.27.2.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.2.3.1.cmml" xref="p1.1.m1.1.27.2.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑢</ci>
              <cn type="integer" id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">2</cn>
            </apply>
            <apply id="p1.1.m1.1.27.2.2.4.cmml" xref="p1.1.m1.1.27.2.2.4">
              <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.2.4.1.cmml" xref="p1.1.m1.1.27.2.2.4">subscript</csymbol>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑢</ci>
              <cn type="integer" id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">3</cn>
            </apply>
          </vector>
          <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑑</ci>
          <apply id="p1.1.m1.1.27.2.3.cmml" xref="p1.1.m1.1.27.2.3">
            <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.3.1.cmml" xref="p1.1.m1.1.27.2.3">subscript</csymbol>
            <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">𝑢</ci>
            <cn type="integer" id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">1</cn>
          </apply>
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝑑</ci>
          <apply id="p1.1.m1.1.27.2.4.cmml" xref="p1.1.m1.1.27.2.4">
            <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.4.1.cmml" xref="p1.1.m1.1.27.2.4">subscript</csymbol>
            <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝑢</ci>
            <cn type="integer" id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑑</ci>
          <apply id="p1.1.m1.1.27.2.5.cmml" xref="p1.1.m1.1.27.2.5">
            <csymbol cd="ambiguous" id="p1.1.m1.1.27.2.5.1.cmml" xref="p1.1.m1.1.27.2.5">subscript</csymbol>
            <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">𝑢</ci>
            <cn type="integer" id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">3</cn>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle dV=\rho(u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}</annotation>
  </semantics>
</math>

SVG (9.5 KB / 3.16 KB) :

d times upper V equals rho times left-parenthesis u 1 comma u 2 comma u 3 right-parenthesis times d times u 1 times d times u 2 times d times u 3

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.57 KB / 391 B) :

d V = ρ ( u 1 , u 2 , u 3 ) d u 1 d u 2 d u 3 {\displaystyle dV=\rho (u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle dV=\rho (u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>d</mi>
        <mi>V</mi>
        <mo>=</mo>
        <mi>&#x03C1;<!-- ρ --></mi>
        <mo stretchy="false">(</mo>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>1</mn>
          </mrow>
        </msub>
        <mo>,</mo>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>2</mn>
          </mrow>
        </msub>
        <mo>,</mo>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>3</mn>
          </mrow>
        </msub>
        <mo stretchy="false">)</mo>
        <mspace width="thinmathspace" />
        <mi>d</mi>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>1</mn>
          </mrow>
        </msub>
        <mspace width="thinmathspace" />
        <mi>d</mi>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>2</mn>
          </mrow>
        </msub>
        <mspace width="thinmathspace" />
        <mi>d</mi>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>3</mn>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle dV=\rho (u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}</annotation>
  </semantics>
</math>

SVG (7.021 KB / 2.847 KB) :

{\displaystyle dV=\rho (u_{1},u_{2},u_{3})\,du_{1}\,du_{2}\,du_{3}}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Volume element page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results