CaLaun

A free, open-source Django calculus tutor that shows step-by-step solutions for derivatives, integrals, and limits. Includes an AI chatbot powered by a self-hosted open-weight LLM (Llama 3.2 3B via Ollama).

Live: https://calaun.org · License: MIT · Status: personal open-source project (not a non-profit;)

Features

• Step-by-step solutions for derivatives, integrals, and limits
• AI chatbot sidebar that explains calculus concepts (powered by self-hosted Ollama; streams per-step answers progressively)
• Reference page with common formulas and "try it" links

Screenshots

The results page shows step-by-step solutions with an AI chatbot sidebar:

• Click any step to expand/collapse details
• Ask the chatbot to explain concepts or clarify steps
• Chatbot is context-aware and sees the current solution

Requirements

• Python 3.9+ (tested with Python 3.12)
• pip
• (Optional) Ollama running locally for the AI chatbot

Setup

1. Create a virtual environment:

   python3 -m venv env
   source env/bin/activate

2. Install dependencies:

   pip install --upgrade pip
   pip install -r requirements.txt

3. Set up the AI chatbot (optional but recommended):

   # Install Ollama from https://ollama.com, then:
   ollama pull llama3.2:3b
   # Set LLM_MODEL=llama3.2:3b in your .env (or whichever model you pulled).
   # LLM_BASE_URL defaults to http://localhost:11434/v1, so no other env vars
   # are needed for local dev.

4. Run the development server:

   python manage.py runserver

5. Visit http://127.0.0.1:8000

Usage

Enter calculus expressions like:

Derivatives:

• diff(x^5, x) - Power rule
• diff(sin(x^2), x) - Chain rule
• diff(x^2 * ln(x), x) - Product rule

Integrals:

• integrate(x^3, x) - Power rule
• integrate(x*exp(x), x) - Integration by parts
• integrate(1/(x^2 - 1), x) - Partial fractions

Limits:

• limit(sin(x)/x, x, 0) - Fundamental trig limit
• limit((1 + 1/x)^x, x, oo) - Definition of e
• limit((x^2 - 4)/(x - 2), x, 2) - Indeterminate form

AI Chatbot

The chatbot talks to any OpenAI-compatible chat-completions endpoint via env vars (LLM_BASE_URL, LLM_API_KEY, LLM_MODEL). Production runs an open-weight model on self-hosted Ollama (currently Llama 3.2 3B). It:

• Explains calculus concepts and rules
• Understands the current solution steps as context
• Streams per-step answers: when the student asks about multiple steps in one message, each step's answer reaches the browser as soon as it's generated, instead of waiting for all of them
• Uses proper LaTeX formatting in responses

See chatbot/README.md for routing details and HTTP API shape.

Testing

python manage.py test        # Run all tests
python -m pytest logic/      # Run logic tests only
python -m pytest chatbot/    # Run chatbot tests only

Tech Stack

• Backend: Django 4.2
• Math Engine: SymPy
• AI Chatbot: Ollama + Llama 3.2 3B (self-hosted, OpenAI-compatible API; NDJSON streaming response)
• Frontend: Vanilla ES6 JavaScript, MathJax 3, CSS custom properties
• Database: SQLite (dev) / PostgreSQL (prod via DATABASE_URL)

Project Structure

├── app/                 # Django app (views, URLs, template tags)
├── chatbot/             # AI chatbot module
│   ├── llm_chat.py      # Chatbot client (OpenAI-compatible, defaults to local Ollama)
│   └── README.md        # Chatbot documentation
├── logic/               # Math solving logic
│   ├── diffsteps.py     # Derivative steps
│   ├── intsteps.py      # Integral steps  
│   ├── limitsteps.py    # Limit steps (including exponential forms)
│   └── resultsets.py    # Result card definitions
├── static/
│   ├── css/modern.css   # Modern CSS with custom properties
│   └── js/app.js        # ES6 JavaScript (ChatSidebar, Collapsible)
├── templates/           # HTML5 templates
└── mathtutor/           # Django settings

License

This project is licensed under the MIT License - see the LICENSE file for details.

Support

If you find this project helpful and want to chip in, you can:

• Use GitHub Sponsors (one-time or recurring)
• Email rbeauvile@calaun.org with any other ideas

CaLaun is a open-source project, not a 501(c)(3), so contributions are not tax-deductible.