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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Euler's Method

In undergraduate math classes, you're taught all these algebraic methods for taking derivatives and integrals and solving differential equations. We didn't mention Laplace transforms, which are even more complicated ways of solving differential equations algebraically. Now, for the dirty secret about differential equations they don't tell you in school, unless you major in engineering: most differential equations you come across in real life have no analytical solution.

The good news is there have been numerical methods for avoiding messy algebra for hundreds of years, and with the invention of computers, these methods have become standard. Even when there is an analytical solution, numerical methods can be almost as accurate for practical purposes as the analytical method and take a fraction of the time to get a solution.

The idea of Euler's method is very simple:

1. Start at the known point.
2. Calculate the derivative at this point...