Interactive Web App & Physics Support

I have two parallel needs and would like to work with one freelancer who can comfortably handle both.

Web-app task
I want a clean, responsive application built with HTML, CSS, JavaScript, and Node.js. The core interactive feature is real-time live-chat messaging, so a lightweight solution such as Socket.io or an equivalent WebSocket approach will be essential. Please set up basic user interface elements, wire the back-end so messages appear instantly across connected clients, and deploy the finished app so I can test it from any browser on desktop and mobile.

Physics & STEM task
Alongside the coding work, I need help tackling advanced physics problems that form part of my current engineering coursework. Typical questions involve technical calculations—think electromagnetism, mechanics, thermodynamics—and I value step-by-step reasoning that makes each solution transparent, not just a final numeric answer.

Deliverables
• Fully functional, hosted Node.js web app with responsive design and live-chat capability
• Source code with clear comments and a short set-up guide
• A document (PDF or Markdown) containing worked physics solutions and explanations for the problem set I provide

Acceptance
I will consider the project complete when the chat updates in real time with no page refresh, the app loads correctly on mobile and desktop, and the physics explanations are thorough enough that I can follow every derivation.