numerical-integration.md

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jupytext kernelspec plotly notebook_metadata_filter text_representation all extension format_name format_version jupytext_version .md markdown 1.1 1.1.1 display_name language name Python 2 python python2 description display_as has_thumbnail language layout name order page_type permalink thumbnail Learn how to integrate a sequence or list of values numerically mathematics false python base Numerical Integration 7 example_index python/numerical-integration/ /images/static-image

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

importplotly.plotlyaspyimportplotly.graph_objsasgofromplotly.toolsimportFigureFactoryasFFimportnumpyasnpimportpandasaspdimportscipy

Integrate the Sine Function

How to use numerical integration to find the area of $y = sin(x)$ between $0$ and $2\pi$.

x=np.linspace(0, 2*np.pi, 100) y=np.sin(x) trace1=go.Scatter( x=x, y=y, mode='lines', ) # use numpy's built in trapezoid-rule integration tooldy=np.trapz(y, x) annotation=go.Annotation( x=4.5, y=1.25, text='Numerical Integration of sin(x) is approximately %s'% (dy), showarrow=False ) layout=go.Layout( annotations=[annotation] ) trace_data= [trace1] fig=go.Figure(data=trace_data, layout=layout) py.iplot(fig, filename='1d-numerical-integration')

fromIPython.displayimportdisplay, HTMLdisplay(HTML('<link href="//fonts.googleapis.com/css?family=Open+Sans:600,400,300,200|Inconsolata|Ubuntu+Mono:400,700" rel="stylesheet" type="text/css" />')) display(HTML('<link rel="stylesheet" type="text/css" href="http://help.plot.ly/documentation/all_static/css/ipython-notebook-custom.css">')) ! pipinstallgit+https://github.com/plotly/publisher.git--upgradeimportpublisherpublisher.publish( 'python_Numerical_Integration.ipynb', 'python/numerical-integration/', 'Numerical Integration | plotly', 'Learn how to integrate a sequence or list of values numerically', title='Numerical Integration in Python. | plotly', name='Numerical Integration', language='python', page_type='example_index', has_thumbnail='false', display_as='mathematics', order=7, ipynb='~notebook_demo/101')