Book description
With examples and activities that help you achieve real results, applying calculus and statistical methods relevant to advanced data science has never been so easy
Key Features
- Discover how most programmers use the main Python libraries when performing statistics with Python
- Use descriptive statistics and visualizations to answer business and scientific questions
- Solve complicated calculus problems, such as arc length and solids of revolution using derivatives and integrals
Book Description
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.
What you will learn
- Get to grips with the fundamental mathematical functions in Python
- Perform calculations on tabular datasets using pandas
- Understand the differences between polynomials, rational functions, exponential functions, and trigonometric functions
- Use algebra techniques for solving systems of equations
- Solve real-world problems with probability
- Solve optimization problems with derivatives and integrals
Who this book is for
If you are a Python programmer who wants to develop intelligent solutions that solve challenging business problems, then this book is for you. To better grasp the concepts explained in this book, you must have a thorough understanding of advanced mathematical concepts, such as Markov chains, Euler's formula, and Runge-Kutta methods as the book only explains how these techniques and concepts can be implemented in Python.
Table of contents
- The Statistics and Calculus with Python Workshop
- Preface
- 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
- Introduction
- Law of Large Numbers
- Central Limit Theorem
- Confidence Intervals
-
Hypothesis Testing
- Parts of a Hypothesis Test
- The Z-Test
- Exercise 9.07: The Z-Test in Action
- Proportional Z-Test
- The T-Test
- Exercise 9.08: The T-Test
- 2-Sample T-Test or A/B Testing
- Exercise 9.09: A/B Testing Example
- Introduction to Linear Regression
- Exercise 9.10: Linear Regression
- Activity 9.01: Standardized Test Performance
- Summary
- 10. Foundational Calculus with Python
-
11. More Calculus with Python
- Introduction
- Length of a Curve
- Length of a Spiral
- Area of a Surface
-
Infinite Series
- Polynomial Functions
- Series
- Convergence
- Exercise 11.09: Calculating 10 Correct Digits of π
- Exercise 11.10: Calculating the Value of π Using Euler's Expression
- A 20th Century Formula
- Interval of Convergence
- Exercise 11.11: Determining the Interval of Convergence – Part 1
- Exercise 11.12: Determining the Interval of Convergence – Part 2
- Exercise 11.13: Finding the Constant
- Activity 11.01: Finding the Minimum of a Surface
- Summary
-
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
- Exercise 12.16: Solving Differential Equations with Euler's Method
- Exercise 12.17: Using Euler's Method to Evaluate a Function
- Runge-Kutta Method
- Exercise 12.18: Implementing the Runge-Kutta Method
- Pursuit Curves
- Exercise 12.19: Finding Where the Predator Catches the Prey
- Exercise 12.20: Using Turtles to Visualize Pursuit Curves
- Position, Velocity, and Acceleration
- Exercise 12.21: Calculating the Height of a Projectile above the Ground
- An Example of Calculating the Height of a Projectile with Air Resistance
- Exercise 12.22: Calculating the Terminal Velocity
- Activity 12.01: Finding the Velocity and Location of a Particle
- 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
Product information
- Title: The Statistics and Calculus with Python Workshop
- Author(s):
- Release date: August 2020
- Publisher(s): Packt Publishing
- ISBN: 9781800209763
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