Courses / Mathematics / Numerical methods and dynamical systems / Project Build and defend your work Build a numerical result you can audit Prepare a reproducible numerical investigation combining an approximation method and a time-evolution model. Declare tolerance, workload and stopping rules, compare with an exact or independently checked case, and demonstrate a failure caused by an invalid setup or coarse step. Use at least two mechanisms; a smooth-looking plot is not validation.
Choose an audience, investigate alternatives, copy evidence from your experiments, and produce an artifact. You can open this project at any time. Reports, numerical transfer checks and human review are separate outcomes.
Your project workspace Choose the kind of work you want to produce School investigation College investigation Workplace application Create an audit notebook with a hand-checked root bracket or integral approximation and a short state-update table. Show how refinement changes the answer and include a deliberately failing step size.
1. Collect and compare evidence Required experiment sources:
Include every source above and at least one pair with different inputs from the same experiment. Explain confounding changes yourself; the presence check does not judge your interpretation.
Open an experiment and change an input or capture a trial to make evidence available here.
2. Write and revise your report Problem and acceptance criteria State the equation or integral, domain, time horizon and desired output accuracy. Define maximum work and a stopping or rejection rule.
Method and intermediate evidence Explain the update or approximation rule and show intermediate brackets, pieces or steps from a capture. Identify assumptions required for its guarantee.
Independent reference and refinement Check a known analytic or independently computed case. Compare at least two resolutions or iteration limits and quantify error instead of relying on visual similarity.
Failure, stability and recovery Demonstrate an invalid bracket, unstable multiplier or unsuitable step size. Explain whether the issue is mathematical setup, approximation error or model behavior, then repair it.
Reproducible conclusion and limits Report parameters, workload, numerical uncertainty and what remains unvalidated about any physical interpretation. For implementation work, provide runnable code and tests separately.
Your artifact: code, analysis, prototype or decision brief This field stores up to 12,000 characters of inert text. Code runs only through the explicit bounded editor in the relevant lessons; project attachments never execute.
Load a text artifact Review your work against the rubric The setup states assumptions, domain and bounded work. Intermediate evidence follows the numerical rule correctly. A reference check and refinement study quantify error. Stability, accuracy and empirical model validity are treated as separate questions. A failing case is diagnosed and repaired without hiding it. 13 evidence requirements remain Capture evidence from Trap a root before approximating it. Capture evidence from Approximate accumulation without hiding its error. Capture evidence from A repeated rule can settle, alternate or grow. Capture evidence from A decaying equation can have a growing approximation. Capture evidence from Read a density as probability per unit. Capture evidence from Connect dynamics estimates and constraints. Include two different input configurations from the same experiment to compare. Write your problem and acceptance criteria. Write your method and intermediate evidence. Write your independent reference and refinement. Write your failure, stability and recovery. Write your reproducible conclusion and limits. Add your project artifact: code, analysis, prototype or decision brief. Record my report Download report and evidence Editing the report or evidence returns it to draft. Recording verifies field presence and input comparisons, not correctness of your reasoning or code.
3. Check transfer to unfamiliar cases These authored cases use different numbers or conditions from the lesson practice. They are public local checks, not secure certification. Each case permits three submissions. Opening, first responses and attempt counts survive imports; no reset creates fresh evidence.
Case numerical-project-bracket Open case numerical-project-bracket Case numerical-project-quadrature Open case numerical-project-quadrature Case numerical-project-recurrence Open case numerical-project-recurrence Case numerical-project-euler Open case numerical-project-euler
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