Metadata
Mathematics Undergraduate Analyze Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Medium

  • Tags

    planar systems, Jacobian, linearization, phase plane, equilibrium, stability

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' ability to analyze stability of equilibrium points in two-dimensional nonlinear ODEs by computing Jacobian matrices, evaluating eigenvalues, classifying equilibria (nodes, saddles, spirals, centers), applying linearization validity (Hartman-Grobman), and using phase-plane tools (nullclines, direction fields, trajectory sketches) to confirm or resolve non-hyperbolic cases.
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Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.