Notebook

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Imports¶

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:

import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Differentiate the Sine Function¶

How to use numerical differentiation to plot the derivative of the sine function $y = sin(x)$:

In [2]:

x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)

dy = np.zeros(y.shape,np.float)
dy[0:-1] = np.diff(y)/np.diff(x)
dy[-1] = (y[-1] - y[-2])/(x[-1] - x[-2])

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='sin(x)'
)

trace2 = go.Scatter(
    x=x,
    y=dy,
    mode='lines',
    name='numerical derivative of sin(x)'
)

trace_data = [trace1, trace2]
py.iplot(trace_data, filename='numerical-differentiation')

Out[2]:

In [3]:

from IPython.display import display, HTML

display(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">'))

! pip install git+https://github.com/plotly/publisher.git --upgrade
import publisher
publisher.publish(
    'python_Numerical_Differentiation.ipynb', 'python/numerical-differentiation/', 'Numerical Differentiation | plotly',
    'Learn how to differentiate a sequence or list of values numerically',
    title='Numerical Differentiation in Python. | plotly',
    name='Numerical Differentiation',
    language='python',
    page_type='example_index', has_thumbnail='false', display_as='mathematics', order=6,
    ipynb= '~notebook_demo/102')

Collecting git+https://github.com/plotly/publisher.git
  Cloning https://github.com/plotly/publisher.git to /private/var/folders/tc/bs9g6vrd36q74m5t8h9cgphh0000gn/T/pip-req-build-OQPV6z
Building wheels for collected packages: publisher
  Running setup.py bdist_wheel for publisher ... done
  Stored in directory: /private/var/folders/tc/bs9g6vrd36q74m5t8h9cgphh0000gn/T/pip-ephem-wheel-cache-RzeGWK/wheels/99/3e/a0/fbd22ba24cca72bdbaba53dbc23c1768755fb17b3af0f33966
Successfully built publisher
Installing collected packages: publisher
  Found existing installation: publisher 0.11
    Uninstalling publisher-0.11:
      Successfully uninstalled publisher-0.11
Successfully installed publisher-0.11

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/IPython/nbconvert.py:13: ShimWarning:

The `IPython.nbconvert` package has been deprecated since IPython 4.0. You should import from nbconvert instead.

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/publisher/publisher.py:53: UserWarning:

Did you "Save" this notebook before running this command? Remember to save, always save.

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