Metadata
Mathematics Graduate Apply Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Apply

  • Difficulty estimate

    Medium

  • Tags

    Lax-Milgram, elliptic PDEs, weak solution, sobolev spaces, coercivity, functional analysis

  • 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 derive weak formulations for second-order elliptic boundary value problems in Sobolev spaces, verify boundedness and coercivity of the associated bilinear form, apply the Lax–Milgram theorem to conclude existence and uniqueness of weak solutions, and obtain basic energy estimates and parameter-dependence for model variable-coefficient problems.
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Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.