Table Of ContentApplying Math with Python
Practical recipes for solving computational math problems
using Python programming and its libraries
Sam Morley
BIRMINGHAM - MUMBAI
Applying Math with Python
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Contributors
About the author
Sam Morley is an experienced lecturer in mathematics and a researcher in pure
mathematics. He is currently a research software engineer at the University of Oxford
working on the DataSig project. He was previously a lecturer in mathematics at the
University of East Anglia and Nottingham Trent University. His research interests lie in
functional analysis, especially Banach algebras. Sam has a firm commitment to providing
high-quality, inclusive, and enjoyable teaching, with the aim of inspiring his students and
spreading his enthusiasm for mathematics.
I would like to thank my friends and colleagues at the University of East Anglia for their
support and encouragement while writing this book. I would also like to thank my editorial
team and the technical reviewers for their hard work.
About the reviewers
Bryan Johns is an experienced data scientist and mathematician. Since completing his PhD
in mathematics, Bryan has been working as a data scientist, where he has been using
Python to deliver machine learning solutions to some of today's most intractable business
problems. Bryan has worked in the financial services and consulting industries, as well as
serving as a data science mentor for the next generation of data scientists. In his free time,
Bryan enjoys surfing, skiing, sailing, and other activities that start with "s." Bryan lives in
San Diego, California, with his wife, one-year-old son, and two mischievous cats.
Valeriy Babushkin is the senior director of data science at X5 Retail Group, where he leads
a team of 80+ people in the fields of machine learning, data analysis, computer vision,
natural language processing, R&D, and A/B testing. Valeriy is a Kaggle competition
grandmaster and attending lecturer at the National Research Institute Higher School of
Economics and the Central Bank of Kazakhstan. He is a technical reviewer of AI Crash
Course and Hands-On Reinforcement Learning with Python, Second Edition, published by Packt.
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Table of Contents
Preface 1
Chapter 1: Basic Packages, Functions, and Concepts 7
Technical requirements 7
Python numerical types 8
Decimal type 8
Fraction type 10
Complex type 10
Basic mathematical functions 10
NumPy arrays 13
Element access 15
Array arithmetic and functions 15
Useful array creation routines 16
Higher dimensional arrays 17
Matrices 19
Basic methods and properties 19
Matrix multiplication 20
Determinants and inverses 22
Systems of equations 24
Eigenvalues and eigenvectors 27
Sparse matrices 29
Summary 31
Further reading 32
Chapter 2: Mathematical Plotting with Matplotlib 33
Technical requirements 34
Basic plotting with Matplotlib 34
Getting ready 35
How to do it... 35
How it works... 36
There's more... 37
Changing the plotting style 39
Getting ready 39
How to do it... 39
How it works... 40
There's more... 41
Adding labels and legends to plots 42
How to do it... 42
How it works... 44
Adding subplots 44
Table of Contents
Getting ready 45
How to do it... 45
How it works... 47
There's more... 47
See also 48
Saving Matplotlib figures 48
Getting ready 48
How to do it... 49
How it works... 49
There's more... 49
See also 50
Surface and contour plots 50
Getting ready 50
How to do it... 50
How it works... 53
There's more... 54
Customizing three-dimensional plots 56
Getting ready 56
How to do it... 56
How it works... 58
There's more... 59
Further reading 59
Chapter 3: Calculus and Differential Equations 60
Technical requirements 61
Working with polynomials and calculus 61
Getting ready 62
How to do it... 62
How it works... 63
There's more... 64
See also 65
Differentiating and integrating symbolically using SymPy 65
Getting ready 65
How to do it... 66
How it works... 67
There's more... 67
Solving equations 68
Getting ready 69
How to do it... 69
How it works... 70
There's more... 71
Integrating functions numerically using SciPy 72
Getting ready 73
How to do it... 73
How it works... 74
[ ii ]
Table of Contents
There's more... 75
Solving simple differential equations numerically 75
Getting ready 76
How to do it... 77
How it works... 78
There's more... 80
See also 80
Solving systems of differential equations 80
Getting ready 81
How to do it... 81
How it works... 84
There's more... 86
Solving partial differential equations numerically 86
Getting ready 87
How to do it... 87
How it works... 90
There's more... 91
See also 93
Using discrete Fourier transforms for signal processing 93
Getting ready 94
How to do it... 94
How it works... 98
There's more... 100
See also 100
Further reading 100
Chapter 4: Working with Randomness and Probability 101
Technical requirements 102
Selecting items at random 102
Getting ready 103
How to do it... 103
How it works... 105
There's more... 106
Generating random data 106
Getting ready 106
How to do it... 107
How it works... 108
There's more... 109
Changing the random number generator 109
Getting ready 109
How to do it... 110
How it works... 110
There's more... 111
Generating normally distributed random numbers 112
Getting ready 112
[ iii ]
