Problem 1
Substitution/residual, known limiting case, conserved quantity, step refinement, alternative solver, dimensional analysis, or comparison with data.
Faculty use
Capstone Computation, Verification and Technical Report
Reward correct mathematics, explicit units, conditions, and hypotheses, interpretation, and verification. Equivalent valid reasoning should receive credit.
Problem 2
Question, context, assumptions, derivation, methods, data, results, verification, sensitivity, limitations, ethics/safety, and conclusion.
Problem 3
Definitions should identify the equation type, dependent and independent variables, parameters, conditions, units or domain, and the hypotheses behind building an auditable chain from derivation to numerical evidence and limitations. Use the formulas analytical benchmark + numerical solution + residual/refinement; sensitivity and scenario comparison.
Problem 4
A strong error analysis identifies the first step that violates classification, algebra, theorem hypotheses, units, initial/boundary data, or numerical assumptions; then repairs that step and re-verifies the final result.
Problem 5
Application responses vary. Require defined variables, a compatible differential-equation model connected to experimental data, engineering design, control, reliability, environmental systems, biomedical modelling, and research communication, a complete computation, interpretation, and limitations.
Problem 6
Accept two independent checks appropriate to the task: differentiation/substitution, initial or boundary conditions, dimensional analysis, phase-line or stability evidence, residuals, step refinement, conservation/energy checks, data comparison, or a second method.
Scoring guidance
Six problems × 10 points: 5 mathematical accuracy, 2 structure/justification, 2 verification/interpretation, 1 notation and communication.