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)

Solving equations

Many mathematical problems eventually reduce to solving an equation of the formf(x) = 0, where f is a function of a single variable. Here, we try to find a value of x for which the equation holds. The values of x for which the equation holds are sometimes called roots of the equation. There are numerous algorithms for finding solutions to equations of this form. In this recipe, we will use the Newton-Raphson and secant methods to solve an equation of the form f(x) = 0.

The Newton-Raphson method (Newton's method) and the secant method are good, standard root finding algorithms that can be applied in almost any situation. These areiterative methods that start with an approximation of the root and iteratively improve this approximation until it lies within a given tolerance.

To demonstrate these techniques, we will use the function from the Symbolic calculus using SymPy recipe defined by

which is defined...