Book Image

Applying Math with Python

By : Sam Morley
Book Image

Applying Math with Python

By: Sam Morley

Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover 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 (12 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...