Jump to content

Search the Community

Showing results for tags 'geometry'.

The search index is currently processing. Current results may not be complete.


More search options

  • Search By Tags

    Type tags separated by commas.
  • Search By Author

Content Type


Categories

  • KTO Matematika
  • Olimpiade Sains
    • Olimpiade Sains Kota
    • Olimpiade Sains Provinsi
    • Olimpiade Sains Nasional
  • Pelatnas IMO Indonesia
    • Tahap I
    • Tahap II
    • Tahap III
  • Lomba Nasional
    • OMITS
    • LM UGM
  • Lomba Regional dan Internasional
  • Lain-lain

Categories

  • Landing

Forums

  • Matematika
    • Pojok Olimpiade
    • Matematika Sekolah
    • Matematika Universitas
  • Kompetisi
    • Olimpiade Sains
    • Pelatnas IMO Indonesia
    • KTO Matematika
  • Nonmatematika
    • Forum Pengumuman
    • Whatever

Found 1 result

  1. (1) Let $f : \mathbb R^3\to \mathbb R$ becomes a smooth function. Prove that $f^{-1}(m_0)$ is 2-dimensional manifolds if $m_0$ is the regular value of $f$. (2) Define $F : \mathbb R^2 \to \mathbb R$ as below, then answer the following questions. $$F(x,y) = x^2 - y^2$$ (a) Scratch the surface of $Gr(F)$. (b) Define $f : Gr(F) \to \mathbb R$ as $f(x,y,z) = z$. Decide whether $f$ is a Morse function. If $f$ is a Morse function, find all the critical points and the Morse index at that points. (3) and (4) to be continued ~
×