# analysis-pde

- Author: Develata
- Repository: Develata/Deve-Skills
- Version: 20260129203735
- Stars: 0
- Forks: 0
- Last Updated: 2026-02-06
- Source: https://github.com/Develata/Deve-Skills
- Web: https://mule.run/skillshub/@@Develata/Deve-Skills~analysis-pde:20260129203735

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# Analysis & Differential Equations Department

**Path**: `math-researcher-teacher/domains/analysis-pde/`

## 🔬 Sub-Domains

### 1. Calculus & Mathematical Analysis (`calculus/`)
*   **Focus**: Rigorous limits ($\epsilon-\delta$), infinite series convergence, multivariable calculus.
*   **Tools**: SymPy for symbolic limits/integrals.

### 2. Real & Complex Analysis (`real-complex/`)
*   **Focus**: Measure theory (Lebesgue), holomorphic functions, contour integration.
*   **Tools**: Symbolic integration, residue calculus.

### 3. Differential Equations (`differential-equations/`)
*   **Focus**: ODEs (existence/uniqueness, stability), PDEs (Heat/Wave/Laplace).
*   **Tools**: `scipy.integrate.solve_ivp` for ODEs, Finite Difference methods for PDEs.

### 4. Functional Analysis (`functional/`)
*   **Focus**: Infinite dimensional spaces, operator theory, distributions.

## 🧭 Routing Instructions

*   If the user asks about **convergence tests** or **rigorous calculus**, check `calculus/`.
*   If the user needs **numerical solutions to equations**, check `differential-equations/`.
*   If the user asks about **complex mappings** or **measure theory**, check `real-complex/`.