Core sequence · 4 modules + 6 legacy chapters
Ordinary Differential Equations
First-order ODEs and modeling, second-order linear ODEs, systems of linear ODEs, and numerical ODE solvers — each with agent-based perspectives on sequential decision-making.
Requires Level 0: Foundations. Continue to Level 2: Partial Differential Equations.
Curriculum Modules
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1.1 — First-Order ODEs and Modeling
Separable, linear, and exact equations. Population growth, radioactive decay, mixing problems, and existence-uniqueness theory.
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1.2 — Second-Order Linear ODEs
Homogeneous and non-homogeneous equations, characteristic equations, undetermined coefficients, variation of parameters, and mechanical/electrical oscillations.
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1.3 — Systems of Linear ODEs
Matrix formulation, eigenvalue methods, phase portraits, stability classification, and coupled oscillator models.
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1.4 — Numerical ODE Solvers
Euler methods, Runge-Kutta family, adaptive step-size control, stiff systems, and error analysis — framed as an agent choosing discretization actions.
Legacy Chapters (Original Material)
01 — Plotting Fundamentals
Graph functions, vector fields, and trajectories to build geometric intuition.
02 — First-Order Equations
Separable, exact, and linear first-order forms with worked symbolic methods.
03 — Higher-Order Equations
Constant-coefficient models and forcing terms with interpretation of solution space.
04 — Linear Systems
Matrix form, eigen-analysis, and phase portraits for coupled dynamics.
05 — Laplace Methods
Transform-domain reasoning for initial-value problems and piecewise inputs.
06 — Series Solutions
Local series expansions and recurrence approaches near ordinary points.