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<!DOCTYPE html>
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<title>MathJax | MathML Samples</title>
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<div id="post-589" class="post-589 page type-page status-publish hentry">
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<h1 class="entry-title">MathML Samples</h1>
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<div class="entry-content">
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<p>This page contains sample equations represented by MathML markup. The page has been configured to always use HTML-CSS mode with web fonts to display the equations, which produces uniform layout and typesetting across browsers.</p>
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<div class="math-header">The Quadratic Formula</div>
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<math display='block'><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mi>b</mi><mo>±</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></math>
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<div class="math-header">Cauchy's Integral Formula</div>
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<math display='block'>
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<mstyle>
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<mi>f</mi>
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<mrow>
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<mo>(</mo>
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<mi>a</mi>
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<mo>)</mo>
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</mrow>
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<mo>=</mo>
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<mfrac>
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<mn>1</mn>
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<mrow>
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<mn>2</mn>
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<mi>π<!-- π --></mi>
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<mi>i</mi>
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</mrow>
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</mfrac>
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<msub>
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<mo>∮</mo>
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<mrow>
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<mi>γ</mi>
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</mrow>
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</msub>
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<mfrac>
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<mrow>
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<mi>f</mi>
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<mo>(</mo>
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<mi>z</mi>
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<mo>)</mo>
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</mrow>
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<mrow>
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<mi>z</mi>
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<mo>−</mo>
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<mi>a</mi>
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</mrow>
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</mfrac>
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<mi>d</mi>
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<mi>z</mi>
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</mstyle>
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</math>
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<div class="math-header">Double angle formula for Cosines</div>
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<math display='block'><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>+</mo><mi>φ</mi><mo>)</mo></mrow><mo>=</mo><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow><mo>−</mo><mi>sin</mi><mo>⁡</mo><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>sin</mi><mo>⁡</mo><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow></mrow></math>
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<div class="math-header">Gauss' Divergence Theorem</div>
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<math display='block'><mrow><mrow><msub><mo>∫</mo><mrow><mi>D</mi></mrow></msub><mrow><mo>(</mo><mo>∇⋅</mo><mi>F</mi><mo>)</mo></mrow><mi>d</mi><mrow><mi>V</mi></mrow></mrow><mo>=</mo><mrow><msub><mo>∫</mo><mrow><mo>∂</mo><mi>D</mi></mrow></msub><mrow><mi>F</mi><mo>⋅</mo><mi>n</mi></mrow><mi>d</mi><mi>S</mi></mrow></mrow></math>
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<div class="math-header">Curl of a Vector Field</div>
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<math display='block'><mrow><mover accent='true'><mrow><mo>∇</mo></mrow><mrow><mo>→</mo></mrow></mover><mo>×</mo><mover accent='true'><mrow><mi>F</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>=</mo><mrow><mo>(</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>z</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>y</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>z</mi></mrow></mfrac><mo>)</mo></mrow><mstyle mathvariant='bold' mathsize='normal'><mrow><mi>i</mi></mrow></mstyle><mo>+</mo><mrow><mo>(</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>x</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>z</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>z</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>x</mi></mrow></mfrac><mo>)</mo></mrow><mstyle mathvariant='bold' mathsize='normal'><mrow><mi>j</mi></mrow></mstyle><mo>+</mo><mrow><mo>(</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>y</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>x</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mo>∂</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>x</mi></mrow></msub></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac><mo>)</mo></mrow><mstyle mathvariant='bold' mathsize='normal'><mrow><mi>k</mi></mrow></mstyle></mrow></math>
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<div class="math-header">Standard Deviation</div>
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<math display='block'><mrow><mi>σ</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mstyle displaystyle='true'><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mrow><msup><mrow><mo stretchy='false'>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><mi>μ</mi><mo stretchy='false'>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></mstyle></mrow></msqrt><mo>.</mo></mrow></math>
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<div class="math-header">Definition of Christoffel Symbols</div>
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<math display='block'><mrow><msup><mrow><mo>(</mo><msub><mrow><mo>∇</mo></mrow><mrow><mi>X</mi></mrow></msub><mi>Y</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msup><msup><mrow><mo stretchy='false'>(</mo><msub><mrow><mo>∇</mo></mrow><mrow><mi>i</mi></mrow></msub><mi>Y</mi><mo stretchy='false'>)</mo></mrow><mrow><mi>k</mi></mrow></msup><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msup><mrow><mo>(</mo><mfrac><mrow><mo>∂</mo><msup><mrow><mi>Y</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow><mrow><mo>∂</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msup></mrow></mfrac><mo>+</mo><msubsup><mrow><mi>Γ</mi></mrow><mrow><mi>i</mi><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msubsup><msup><mrow><mi>Y</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow></mrow></math> </div><!-- .entry-content -->
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