The Leanpub 60 Day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
See full terms...
The Computational Pendulum: From Classical Mechanics to Neural Networks
This book is 50% completeLast updated on 2026-10-20
The ultimate bridge from high school AP Physics to modern AI. Start with the familiar physics you know, translate it into Python, and use it as a launchpad to build advanced Machine Learning models and neural networks. Includes 100% solved exercises and click-to-run Google Colab labs.
Minimum price
$19.99
$29.99
You pay
Author earns
PDF
304
Pages
About
About the Book
Most textbooks present math and physics as rigid formulas on flat paper. This book changes that by introducing Computational Physics—the exact blend of advanced mathematics, physics, and software engineering used by researchers at NASA, SpaceX, and top data science labs.
Designed explicitly for upper high school students (Grades 10-12), advanced middle schoolers, and tech-forward homeschool collectives, this workbook bridges the gap between theoretical calculations and practical software execution.
🗂️ How the Book is Structured: A 3-Stage Pipeline
- Phase 1: The High School Runway (First 35% — Most of it Available Now): Perfect for AP Physics students and coding beginners. We start with standard AP-level mechanics, kinematics, and energy conservation. Instead of just solving these equations on paper, students learn how to convert them into foundational Python code.
- Phase 2: The Numerical Leap (In Progress): Stepping into university-level computational physics. We strip away the over-simplified "small-angle approximations" found in standard textbooks. Students learn why standard math breaks down in the real world and how to solve complex dynamical systems using heavy numerical tools like 4th-order Runge-Kutta (RK4) integration and Fast Fourier Transforms (FFT).
- Phase 3: The AI Destination (In Progress): Building a standout modern portfolio. We use our trusted pendulum model as a transparent baseline to explore modern artificial intelligence. Students will build and train Physics-Informed Neural Networks (PINNs) in JAX, discover physical laws directly from raw data, and explore cutting-edge concepts like Reservoir Computing.
💡 Why Buy the In-Progress Edition Today?
This is a living curriculum currently in active development. By purchasing the in-progress book today, you lock in the lowest possible price. As new chapters, calculus projects, and physics models are added, the minimum price of this book will scale upward. Buying today ensures you get all future updates entirely for free.
Author
About the Author
Horos Kyklos
HOROS KYKLOS holds advanced degrees in physics and computer science and has worked in both academia and the software industry. Having spent years navigating theoretical research and production software engineering, Kyklos writes with a focus on uniting mathematical rigor with modern computation. THE COMPUTATIONAL PENDULUM grew out of a desire to tear down the artificial walls between analytical physics, numerical simulation, and machine learning—showing students, educators, and developers how a single physical system can illuminate all three.
Get the free sample chapters
Click the buttons to get the free sample in PDF or EPUB, or read the sample online here
Earn $8 on a $10 Purchase, and $16 on a $20 Purchase
We pay 80% royalties on purchases of $7.99 or more, and 80% royalties minus a 50 cent flat fee on purchases between $0.99 and $7.98. You earn $8 on a $10 sale, and $16 on a $20 sale. So, if we sell 5000 non-refunded copies of your book for $20, you'll earn $80,000.
(Yes, some authors have already earned much more than that on Leanpub.)
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
Write and Publish on Leanpub
You can use Leanpub to easily write, publish and sell in-progress and completed ebooks and online courses!
Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks.
Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. (Or, if you are producing your ebook your own way, you can even upload your own PDF and/or EPUB files and then publish with one click!) It really is that easy.