Applied collegiate investigation

Integrated Design: Area, Volume & Surface Optimization

How do geometry, slicing, rotation, and metric formulas turn integral setup into defensible area, volume, length, and surface models?

Investigation brief

Design or analyze a model involving design, manufacturing, architecture, material estimation, and geometric modelling. 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
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