Real Analysis

ℝeal Analysis

ℝeal Analysis

Juan Carlos Ponce Campuzano

Juan Carlos
Ponce Campuzano


Introduction

Welcome to the fascinating world of real analysis, where math leaps off the page through interactive visuals. In this book, we break free from the ordinary, offering an immersive exploration of real analysis principles with engaging visualizations.

Real analysis isn't just math; it's a key to unlocking the structure of the mathematical universe. Thanks to technology, we're bringing abstract ideas to life with interactive tools, creating a tangible learning experience.

As you journey through this book, discover a mix of theory and interactive tools designed for a deep understanding of real analysis. From limits to sequences, each chapter unfolds with visualizations, turning abstract concepts into an interactive landscape.

Whether you're a first-time explorer or a seasoned math traveler, our approach empowers you to grasp complex ideas intuitively. Visualizations here aren't just aids; they're windows into the elegance that defines real analysis.

Join me in this enlightening adventure, where math concepts come alive, bridging the gap between theory and intuition. Let's navigate through the visual landscapes of real analysis, turning abstract ideas into tangible insights and fostering a profound appreciation for the beauty of mathematics.

It is by logic that we prove, but by intuition that we discover. — Henri Poincaré

Table of Contents

  1. The real numbers 🚧
  2. Sequences
  3. Series 🚧
  4. Limits of functions
  5. Continuity of functions
  6. The Derivative 🚧
  7. The Riemann integral 🚧
  8. Sequences of functions 🚧
  9. Metric spaces & Topology 🚧

Credits

The designed of this website was inspired by these projects:

And it was built using amazing open-source software:


Note! This project is still under construction 🏗️. It exists thanks to the support of my patreons:
Edward Huff, Abei, pmben, Sophia Wood (Fractal Kitty), Adam Parrott, Doug Kuhlmann, bleh, Miguel Díaz, Ruan Ramon, Maciej Lasota, Christopher-Alexander Hermanns, Aarón Reyes, Gabriela Sofia Marin Sanchez, Jerome Siegler, Yashar Shoraka, Jeff Butterworth, Shaun MacMillan, Ihsan Karabulut, Elias Sanchez Angarano.
If you find this project worthwhile, please consider becoming a member in Patreon. ♾️ Thanks!