Problem 1
Yes; outputs may strongly depend on a combination of parameters that data cannot separate.
Faculty use
Sensitivity, Identifiability and Uncertainty
Reward correct mathematics, explicit units, conditions, and hypotheses, interpretation, and verification. Equivalent valid reasoning should receive credit.
Problem 2
Measurement error, parameter variability, model-form error, initial-condition uncertainty, and numerical error.
Problem 3
Definitions should identify the equation type, dependent and independent variables, parameters, conditions, units or domain, and the hypotheses behind distinguishing parameter influence from the ability to infer parameters uniquely. Use the formulas S_p=∂y/∂p; propagate uncertainty through model outputs.
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.