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)

Solving differential equations using JAX

JAX provides a set of tools for solving a wide array of problems. Solving differential equations—such as initial value problems described in the Solving simple differential equations numerically recipe—should be well within the capabilities of this library. The diffrax package provides various solvers for differential equations leveraging the power and convenience of JAX.

In the earlier recipe, we solved a relatively simple first-order ODE. In this recipe, we’re going to solve a second-order ODE to illustrate the technique. A second-order ODE is a differential equation that involves both the first and second derivatives of a function. To keep things simple, we’re going to solve a linear second-order ODE of the following form:

Here, is a function of to be found. In particular, we’re going to solve the following equation:

The initial conditions are and...