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)

Using least squares to fit a curve to data

Least squares is a powerful technique for finding a function from a relatively small family of potential functions that best describe a particular set of data. This technique is especially common in statistics. For example, least squares is used in linear regression problems – here, the family of potential functions is the collection of all linear functions. Usually, the family of functions that we try to fit has relatively few parameters that can be adjusted to solve the problem.

The idea of least squares is relatively simple. For each data point, we compute the square of the residual – the difference between the value of the point and the expected value given a function – and try to make the sum of these squared residuals as small as possible (hence, least squares).

In this recipe, we’ll learn how to use least squares to fit a curve to a sample set of data.

Getting ready

For this recipe, we will need...