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)

Calculus and Differential Equations

In this chapter, we will discuss various topics related to calculus. Calculus is the branch of mathematics that concerns the processes of differentiation and integration. Geometrically, the derivative of a function represents the gradient of the curve of the function, and the integral of a function represents the area below the curve of the function. Of course, these characterizations only hold in certain circumstances, but they provide a reasonable foundation for this chapter.

We’ll start by looking at calculus for a simple class of functions: polynomials. In the first recipe, we’ll create a class that represents a polynomial and define methods that differentiate and integrate the polynomial. Polynomials are convenient because the derivative or integral of a polynomial is again a polynomial. Then, we’ll use the SymPy package to perform symbolic differentiation and integration on more general functions. After that, we’...