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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

# Calculating Integrals

1. One major topic of calculus is differential calculus, which means taking derivatives, as we've been doing so far in this chapter. The other major topic is integral calculus, which involves adding up areas or volumes using many small slices.

When calculating integrals by hand, we're taught to reverse the algebra we would do to find a derivative. But that algebra gets messy and, in some cases, impossible. The hard version we learned in school was Riemann sums, which required us to cut the area under a curve into rectangular slices and add them up to get the area. But you could never work with more than 10 slices in a realistic amount of time, certainly not on a test.

However, using Python, we can work with as many slices as we want, and it saves us the drudgery of jumping through a lot of hoops to get an algebraic equation. The point of finding the algebraic equation is to obtain accurate number values, and if using a program will get us the most accurate numbers...