5 (1)

5 (1)

#### 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

# Mixture Problems

In algebra, there are word problems where you have to figure out how much material you have to add to a mixture to get a certain concentration or amount. In calculus, naturally, the problem has to be harder: for example, the mixture is changing; material is going into the mixture, and material is going out. You have to find out how much mixture or how much of the solvent is present after a specific amount of time. Let's look at the following exercise to better understand this concept.

## Exercise 12.12: Solving Mixture Problems – Part 1

A tank contains 82 gallons of brine in which 18 pounds of salt is dissolved. Brine containing 3 pounds of dissolved salt per gallon flows into the tank at the rate of 5 gallons per minute. The mixture, which is kept uniform by stirring, flows out of the tank at a rate of 2 gallons per minute. How much salt is in the tank at the end of 39 minutes?

As you can imagine, this kind of problem leads to some complicated differential...