noc20 ma01 lec05 Inverse Function Theorem

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  • Опубликовано: 10 янв 2025

Комментарии • 3

  • @shampanchal4414
    @shampanchal4414 3 года назад

    Note: A local homeomorphism is still available if one assumes everywhere differentiability of the function on the domain although the result is a bit complicated. For reference visit terry tao’s blog which has a good explanation on it.

  • @pde9322
    @pde9322 4 года назад

    Sir, what is the difference between C1 and C2 function?

    • @MathwithMing
      @MathwithMing 3 года назад +4

      A function is C^k if its k-th order derivative exists and is continuous. Thus, C^1 functions are continuously differentiable and C^2 functions are twice continuously differentiable. For example, f(x)=x^{4/3} is C1 but not C2 on R, since its second-order derivative is discontinuous at x=0.