#!/usr/bin/env python
# coding: utf-8

# > This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.
# 

# # 15.3. Analyzing real-valued functions

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from sympy import *
init_printing()


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var('x z')


# We define a new function depending on x.

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f = 1/(1+x**2)


# Let's evaluate this function in 1.

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f.subs(x, 1)


# We can compute the derivative of this function...

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diff(f, x)


# limits...

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limit(f, x, oo)


# Taylor series...

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series(f, x0=0, n=9)


# Definite integrals...

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integrate(f, (x, -oo, oo))


# indefinite integrals...

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integrate(f, x)


# and even Fourier transforms!

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fourier_transform(f, x, z)


# > You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).
# 
# > [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (500 pages).