Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (13 chapters)

Differentiating and integrating symbolically using SymPy

At some point, you may have to differentiate a function that is not a simple polynomial, and you may need to do this in some kind of automated fashion—for example, if you are writing software for education. The Python scientific stack includes a package called SymPy, which allows us to create and manipulate symbolic mathematical expressions within Python. In particular, SymPy can perform differentiation and integration of symbolic functions, just like a mathematician.

In this recipe, we will create a symbolic function and then differentiate and integrate this function using the SymPy library.

Getting ready

Unlike some of the other scientific Python packages, there does not seem to be a standard alias under which SymPy is imported in the literature. Instead, the documentation uses a star import at several points, which is not in line with the PEP8 style guide. This is possibly to make the mathematical expressions...