📊 Multivariable Function Analyzer

A modular FastAPI + JavaScript frontend application that analyzes and visualizes multivariable functions. It computes critical points, classifies them using gradient & Hessian analysis, and generates 3D surface plots and 2D contour plots with gradient vectors — all accessible via clean REST endpoints. Built as part of my weekly computer science learning journey, this project focuses on calculus automation, backend architecture, and interactive data visualization.

🎯 Learning Goals

This week’s focus:

• REST API Design — Structuring mathematical analysis endpoints in FastAPI
• Symbolic Computation — Using SymPy for gradient, Hessian, and critical point classification
• Data Visualization — Generating 3D and 2D plots with Matplotlib
• Frontend–Backend Integration — Connecting a static JS frontend to a Python API
• Testing & Validation — Using pytest to verify mathematical correctness

🚀 Features

• Critical Point Analysis — Finds and classifies local minima, maxima, and saddle points
• Degenerate Hessian Handling — Higher‑order term checks for flat curvature cases
• 3D Surface Plotting — Interactive‑ready PNGs generated on the fly
• 2D Contour + Gradient Vectors — Visualizes function topology and direction of steepest ascent
• Multi‑Point Support — Handles functions with multiple distinct critical points
• Test Suite — Parametrized pytest cases for robust verification

📦 Tech Stack

• Python 3.12 — Backend runtime
• FastAPI — API framework
• SymPy — Symbolic math engine
• NumPy — Numerical computation
• Matplotlib — Plot generation
• Pytest — Automated testing
• Vanilla JS + HTML/CSS — Lightweight frontend

🏗️ How It Works

• Backend (backend/)
• math_utils.py — Gradient, Hessian, classification logic
• plot_utils.py — 3D surface & 2D contour plot generation
• main.py — FastAPI routes for /analyze and /plot
• CORS middleware for cross‑origin frontend requests
• Frontend (frontend/)
• index.html — UI layout
• script.js — Fetch calls to backend, DOM updates
• style.css — Basic styling
• Tests (backend/test_math_utils.py)
• Covers local min/max/saddle, degenerate Hessians, and multi‑point cases

📚 Part of My Learning Journey

This project is part of my ongoing exploration of computer science concepts. Each week, I pick a new topic or technology to dive into through hands‑on projects. This week: Symbolic math automation and visualization with FastAPI. Previous weeks have included:

• Backend API design with Node.js & Express
• Cloud deployment with Azure Functions
• SQL optimization and data modeling
• React Native gesture‑based UI development The goal is to continuously expand my CS knowledge through practical implementation.

🎓 What I Learned

• How to compute and classify critical points programmatically
• Handling degenerate Hessians with higher‑order analysis
• Generating and encoding plots for API delivery
• Structuring a Python backend for modularity and testability
• Connecting a static JS frontend to a Python API with CORS

⚠️ Educational Purpose

This project is designed for educational purposes and learning about multivariable calculus automation. Always verify mathematical results before using them in critical applications.

Built with 💻 Python, FastAPI, and a passion for learning something new every week.