Problem 1
Command of model construction, solution method, parameter meaning, verification, limitations, and ability to respond to alternatives.
Faculty use
Oral Defense and Advanced Differential-Equations Bridge
Reward correct mathematics, explicit units, conditions, and hypotheses, interpretation, and verification. Equivalent valid reasoning should receive credit.
Problem 2
Partial differential equations, nonlinear dynamics, control theory, numerical analysis, stochastic differential equations, mathematical biology, or continuum mechanics.
Problem 3
Definitions should identify the equation type, dependent and independent variables, parameters, conditions, units or domain, and the hypotheses behind defending choices and mapping next study into PDEs, dynamical systems, control, and numerical analysis. Use the formulas claim ↔ equation ↔ evidence ↔ limitation; advanced study extends theory and computation.
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.