Multiple Integrals & ODEs
Double and triple integrals over rectangular regions, and ordinary differential equations — exact solutions where structure allows, Runge–Kutta solution families everywhere else. Covers §5.34–5.37.
∬ f(x,y) dA and ∭ f(x,y,z) dV over a Box
Integration region. FIG. T32-1
y′ + a·y = b — Exact by Integrating Factor
General y′ = f(x, y) — RK4 Solution Family
Each curve is the RK4 solution from one initial value — the family shows how solutions flow. FIG. T33-1
a·y″ + b·y′ + c·y = 0 — Characteristic Equation
Sample solution with C₁ = C₂ = 1 — decay, oscillation, or both, depending on the discriminant. FIG. T33-2