This is one of the 100 recipes of the IPython Cookbook, 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, by Cyrille Rossant, Packt Publishing, 2014 (500 pages).