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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

# Equations

Again, an equation is formed when a function is assigned the value 0 and we are asked to find the values of the function input, normally x, that satisfy the equation. These values are called the roots of the original function. The process of finding these values is called solving an equation, which is a rich topic in mathematics and, specifically, algebra.

In this section, we will discuss two fundamental methods of solving equations by hand as well as examine the available computational tools in Python to facilitate the process of automatically solving equations. We will start with the first method, algebraic manipulations.

## Algebraic Manipulations

While we are classifying this as a method, algebra is, in general, a technique to translate an equation to a simpler form so that solutions can be found easily. Some typical ways to translate an equation are adding/subtracting a constant to both sides of the equation, multiplying/dividing both sides by a non-zero constant...