Intermediate–Advanced · 3 modules + 7 legacy chapters

Partial Differential Equations

Scalar PDE classification, numerical methods (finite differences, finite elements, spectral methods), and stochastic and complex models — with agent-based perspectives on solver decision-making.

Requires Level 1: ODEs. Continue to Level 3: AI-Driven Methods.

Curriculum Modules

  1. 2.1 — Scalar PDEs and Classification

    Elliptic, parabolic, and hyperbolic PDEs. Heat equation, wave equation, Laplace equation, separation of variables, and Fourier series solutions.

    Intermediate · 5–6 Hours

  2. 2.2 — Numerical PDE Methods

    Finite difference methods, stability analysis (CFL condition, von Neumann analysis), finite element introduction, and spectral methods overview.

    Advanced · 5–6 Hours

  3. 2.3 — Stochastic and Complex Models

    Stochastic differential equations, Brownian motion, Ito calculus, Monte Carlo methods, and coupled multi-physics systems.

    Advanced · 4–5 Hours

Legacy Chapters (Original Material)

  1. 00 — Linear Algebra Review

    Core matrix tools, eigen-structure, and decomposition techniques for DE analysis.

    Foundation · 2–3 Hours

  2. 01 — Advanced Linear Algebra

    Spectral viewpoints and transforms supporting high-dimensional systems.

    Intermediate · 4 Hours

  3. 02 — Systems of ODEs

    Qualitative dynamics, phase space, and stability for coupled equations.

    Intermediate · 4–5 Hours

  4. 03 — Fourier Series

    Orthogonal expansions and boundary-value structure in periodic settings.

    Intermediate · 4 Hours

  5. 04 — Partial Differential Equations

    Separation of variables for wave, heat, and Laplace-type equations.

    Advanced · 5 Hours

  6. 05 — Numerical Methods

    Discretization, convergence, and implementation strategies for PDE solvers.

    Advanced · 5 Hours

  7. 06 — Independent Projects

    Applied synthesis projects combining analysis, coding, and interpretation.

    Advanced · 5+ Hours