Vector Calculus is a powerful branch of mathematics that extends traditional calculus into multiple dimensions. It enables the study of phenomena involving direction and magnitude, and serves as the mathematical foundation for fields such as physics, engineering, and computer graphics, where understanding how quantities change in space is crucial.
This interactive book combines theoretical concepts with dynamic visualizations to provide a hands-on approach to learning Vector Calculus. Unlike traditional textbooks, this online resource integrates interactive applets to help you visualize complex concepts in a way that bridges intuition with mathematical rigor. You will be able to explore the geometry of vectors is space, parametric surfaces, vector fields, gradients, divergence, curl, line and surface integrals, among other topics, through engaging simulations. These applets are built using open-source tools such as GeoGebra, Desmos, Math3D, p5.js, Three.js, MathBox, and MathCell.js.
As you work through the material, you'll gain a deeper understanding of the subject and appreciate both its beauty and its practical applications in real-world scenarios.
Note! This project is still under construction 🏗️.
It exists thanks to the support of my patrons:
Edward Huff, Abei, pmben, Sophia Wood (Fractal Kitty),
Adam Parrott, Doug Kuhlmann, Dennis Watson, bleh,
Miguel Díaz, Ruan Ramon, Maciej Lasota,
Christopher-Alexander Hermanns, Aarón Reyes,
Gabriela Sofia Marin Sanchez, Jerome Siegler,
Yashar Shoraka, Jeff Butterworth,
Scott Pedersen, Ihsan Karabulut,
Elias Sanchez Angarano, Emanuel Silva.
If you find this project worthwhile, please consider becoming a member in
Patreon.
♾️ Thanks!