Applied collegiate investigation

Dynamic-System Model & Parameter Defense

How do direction fields, exact methods, numerical methods, and parameter evidence describe systems that change over time?

Investigation brief

Design or analyze a model involving population, cooling, mixing, finance, medicine, circuits, and resource systems. Define a question that requires the unit’s mathematics, identify data or defensible assumptions, derive the model, compute or approximate a result, validate it independently, and state limitations.

Required submission

  1. Question, context, diagram, variables, units, and assumptions.
  2. Mathematical derivation with theorem or method justification.
  3. Exact and/or numerical result with technology record.
  4. Error, sensitivity, residual, or convergence evidence.
  5. Interpretation, limitations, and next research question.

Oral defense prompts

  • Why is this method valid?
  • What alternative did you reject?
  • How did you verify the result?
  • Which assumption matters most?
  • How would the model change?

20-point rubric

Criterion4 · Exemplary3 · Proficient2 · Developing1 · Incomplete
Model and assumptionsPrecise, justified, dimensionalMostly completeImportant gapsUnclear
Calculus reasoningComplete and rigorousCorrect with minor gapsPartialUnsupported
VerificationIndependent and quantifiedMeaningful checkWeak checkAbsent
InterpretationContextual and nuancedClearLimitedMissing
CommunicationProfessional and defensibleOrganizedUnevenUnclear
β Beta Program