Thinking in Calculus

An intuitive, Python-based introduction to calculus for readers interested in real applications of the math.

Many people take a calculus course and walk away remembering almost nothing—except vague ideas about slopes, curves, and something called a tangent.

Thinking in Calculus is written for those readers, as well as anyone else with a firm grasp of algebra and trigonometry who is eager to learn the practical math underlying machine learning optimization, signals processing, planetary simulations, and other useful applications.

Rather than teaching calculus as a collection of formulas and procedures, this book uses guided Jupyter Notebooks to introduce concepts like derivatives, integrals, the Fundamental Theorem, and dynamical systems through visualizations and real-world examples.

Designed for curious self-learners, programmers, and students who want to understand what calculus is actually describing, Thinking in Calculus rebuilds the subject from the inside out— patiently and in context.Foreword
Acknowledgments
Introduction

Chapter 1: Python Basics
Chapter 2: Drawing with Turtle Graphics
Chapter 3: Functions and Derivatives
Chapter 4: Integrals
Chapter 5: Ordinary Differential Equations and Vectors
Chapter 6: Dynamical Systems
Chapter 7: Linear Algebra with NumPy
Chapter 8: Multivariable Calculus
Chapter 9: Fourier Transforms

Appendix A
Bibliography
IndexNick McIntyre is an experienced educator who designs learning experiences around clarity, intuition, and curiosity. His background in teaching mathematics, robotics, and computer science informs an approach that treats calculus as something to be explored and understood—not endured.