Boundary-Driven Cancellation in Vector Field Integrals
Deliverables
- Derivation & Diagrams.md
- Snippets.rar
- Animations.rar
Summary
These files provide a comprehensive pedagogical structure for investigating boundary-driven cancellation in vector field integrals, specifically addressing the mathematical challenges of power-law singularities. Through a series of four interconnected demonstrations, the project guides learners from analytical proofs—using the Divergence Theorem to identify scalar field potential—to advanced visual simulations that contrast finite, well-behaved flux against divergent "blow-up" scenarios. By establishing a state-machine architecture that enforces an "exclusion zone" around the origin, the framework ensures analytical stability while using dimensional projections and high-contrast heatmap visualizations to make complex gradient dynamics and potential wells intuitively accessible.
CDP