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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

Solving Linear Equations Using Matrices

Linear equations are the foundational blocks of algebra, and anyone who has studied basic elementary mathematics knows how they work. Let's cover them briefly, and we can then see how easily they can be solved using matrices in Python.

Linear equations are typically in the form:

Figure 6.5: Formula for calculating linear equations

Here, a1, a2,.., an are the coefficients, and x1, x2,.. xn are variables.

These linear equations with two variables can be represented in a two-dimensional space graph where x is the horizontal dimension and y is the vertical dimension.

Let's take a quick example of a linear equation with two variables. Suppose the equation is y = 2x + 6. This representation is known as the slope-intercept form and has the format y = mx + c, where m is the slope and c is the y intercept of the equation.

Here, m=2 and c=6, and the line can be drawn on a graph by plotting different values...