Book Image

The Statistics and Calculus with Python Workshop

By : Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, Marios Tsatsos
5 (1)
Book Image

The Statistics and Calculus with Python Workshop

5 (1)
By: Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, Marios Tsatsos

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.

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Table of Contents (14 chapters)
Preface
About the Book
1
1. Fundamentals of Python
1. Fundamentals of Python
Introduction
Control Flow Methods
Data Structures
Functions and Algorithms
Testing, Debugging, and Version Control
Summary
Free Chapter
2
2. Python's Main Tools for Statistics
2. Python's Main Tools for Statistics
Introduction
Scientific Computing and NumPy Basics
Working with Tabular Data in pandas
Data Visualization with Matplotlib and Seaborn
Summary
3
3. Python's Statistical Toolbox
3. Python's Statistical Toolbox
Introduction
An Overview of Statistics
Types of Data in Statistics
Descriptive Statistics
Inferential Statistics
Python's Other Statistics Tools
Summary
4
4. Functions and Algebra with Python
4. Functions and Algebra with Python
Introduction
Functions
Function Transformations
Equations
Systems of Equations
Summary
5
5. More Mathematics with Python
5. More Mathematics with Python
Introduction
Sequences and Series
Trigonometry
Vectors
Complex Numbers
Summary
6
6. Matrices and Markov Chains with Python
6. Matrices and Markov Chains with Python
Introduction
Matrix Operations on a Single Matrix
Operations on Multiple Matrices
Solving Linear Equations Using Matrices
Transition Matrix and Markov Chains
Summary
7
7. Doing Basic Statistics with Python
7. Doing Basic Statistics with Python
Introduction
Data Preparation
Calculating and Using Descriptive Statistics
Exploratory Data Analysis
Summary
8
8. Foundational Probability Concepts and Their Applications
8. Foundational Probability Concepts and Their Applications
Introduction
Randomness, Probability, and Random Variables
Discrete Random Variables
Continuous Random Variables
Summary
9
9. Intermediate Statistics with Python
9. Intermediate Statistics with Python
Introduction
Law of Large Numbers
Central Limit Theorem
Confidence Intervals
Hypothesis Testing
Summary
10
10. Foundational Calculus with Python
10. Foundational Calculus with Python
Introduction
Writing the Derivative Function
Calculating Integrals
Using Trapezoids
Using Integrals to Solve Applied Problems
Using Derivatives to Solve Optimization Problems
Summary
11
11. More Calculus with Python
11. More Calculus with Python
Introduction
Length of a Curve
Length of a Spiral
Area of a Surface
Infinite Series
Summary
12
12. Intermediate Calculus with Python
12. Intermediate Calculus with Python
Introduction
Differential Equations
Interest Calculations
Population Growth
Half-Life of Radioactive Materials
Newton's Law of Cooling
Mixture Problems
Euler's Method
Summary
Appendix
1. Fundamentals of Python
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...

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