🧄Solution and Proof for a Vector Identity and Divergence Problem

This app is an interactive educational tool that uses a visualizer to demonstrate and verify key vector calculus concepts. It showcases Euler's Homogeneous Function Theorem for vector fields, proving the identity $(x \cdot \nabla) v=n v$ for different homogeneous vector fields. The tool further applies this principle to compute the divergence of a more complex vector expression, simplifying $\nabla \cdot{x[x \cdot v]}$ to $(n+4)(x \cdot v)$. By bridging abstract theory with a dynamic, real-time visualization and calculation, the app makes complex mathematical relationships tangible and easy to understand.

🎬the Homogeneous Function Theorem for vector fields

This app is a teaching tool that visualizes and verifies the Homogeneous Function Theorem for vector fields. It shows how different vector fields behave and proves that the identity $( x \nabla) v=n v$ holds true for each one. The demo lets you see abstract math concepts come to life with real-time calculations.

🖊️Mathematical Proof

Solution and Proof for a Vector Identity and Divergence Problem | Proof and Derivationviadean on Notion