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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

# Area of a Surface

Let's learn how to take this from two to three dimensions and calculate the area of a 3D surface. In Chapter 10, Foundational Calculus with Python, we learned how to calculate the area of a surface of revolution, but this is a surface where the third dimension, z, is a function of the values of x and y.

## The Formulas

The traditional, algebraic way to solve this analytically is given by a double integral over a surface:

Figure 11.18: Formula to calculate area of a surface

Here, z = f(x,y) or (x,y,f(x,y)). Those curly d's are deltas, meaning we'll be dealing with partial derivatives. Partial derivatives are derivatives but only with respect to one variable, even if the function is dependent on more than one variable. Here's a function that returns the partial derivative of a function, `f`, with respect to a variable, `u`, at a specific point (`v,w`). Depending on which variable we're interested in, x or y, the function...