Math / Continuation Stub
Numerical methods keep the conversation moving when exact form breaks down.
This is a deliberate stub. Many important systems do not yield to one clean symbolic answer, but they still invite disciplined approximation. Numerical methods give names to that discipline: step size, convergence, stability, truncation error, and iteration count. This route exists so the handoff from slope fields and integration techniques stays visible.
Useful First Questions
Step size
How much local error does one step introduce, and what happens when the step is too coarse for the shape of the problem?
Convergence
Does the repeated procedure home in on a stable answer, oscillate, or wander away?
Stability
Does a small perturbation stay bounded, or does the numerical procedure amplify it until the answer stops meaning anything?
Why this matters
Approximation methods are where calculus, differential equations, and algorithm literacy stop being separate subjects and start becoming engineering practice.