Problem 1
Concentration is uniform at every instant and outflow concentration equals tank concentration; flow rates are known.
Faculty use
Assumptions, Calibration and Sensitivity in Applied Models
Reward correct mathematics, explicit units, conditions, and hypotheses, interpretation, and verification. Equivalent valid reasoning should receive credit.
Problem 2
Perturb each parameter within a justified range and compare changes in predicted outputs or decision thresholds.
Problem 3
Definitions should identify the equation type, dependent and independent variables, parameters, conditions, units or domain, and the hypotheses behind testing whether parameters, data, and idealizations support the intended conclusion. Use the formulas residual=observed−predicted; sensitivity S_p=∂output/∂p.
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 thermal systems, tanks and reactors, mechanics, ecology, pharmacology, and electrical circuits, 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.