The Differentiable Functions from R into R n

Keiko Narita; Artur Korniłowicz; Yasunari Shidama

Formalized Mathematics (2012)

  • Volume: 20, Issue: 1, page 65-71
  • ISSN: 1426-2630

Abstract

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In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.

How to cite

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Keiko Narita, Artur Korniłowicz, and Yasunari Shidama. " The Differentiable Functions from R into R n ." Formalized Mathematics 20.1 (2012): 65-71. <http://eudml.org/doc/268281>.

@article{KeikoNarita2012,
abstract = {In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.},
author = {Keiko Narita, Artur Korniłowicz, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {65-71},
title = { The Differentiable Functions from R into R n },
url = {http://eudml.org/doc/268281},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Keiko Narita
AU - Artur Korniłowicz
AU - Yasunari Shidama
TI - The Differentiable Functions from R into R n
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 1
SP - 65
EP - 71
AB - In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.
LA - eng
UR - http://eudml.org/doc/268281
ER -

References

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  1. Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  3. Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  4. Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  5. Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  6. Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  7. Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  8. Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  9. Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  10. Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  11. Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005. 
  12. Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.[Crossref] 
  13. Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. 
  14. Takao Inoué, Adam Naumowicz, Noboru Endou, and Yasunari Shidama. Partial differentiation of vector-valued functions on n-dimensional real normed linear spaces. Formalized Mathematics, 19(1):1-9, 2011, doi: 10.2478/v10037-011-0001-x.[Crossref] Zbl1276.26033
  15. Keiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.[Crossref] 
  16. Keiko Narita, Artur Kornilowicz, and Yasunari Shidama. More on the continuity of real functions. Formalized Mathematics, 19(4):233-239, 2011, doi: 10.2478/v10037-011-0032-3.[Crossref] Zbl1276.26006
  17. Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. 
  18. Hiroyuki Okazaki, Noboru Endou, Keiko Narita, and Yasunari Shidama. Differentiable functions into real normed spaces. Formalized Mathematics, 19(2):69-72, e2011, doi: 10.2478/v10037-011-0012-7.[Crossref] Zbl1276.26035
  19. Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011, doi: 10.2478/v10037-011-0008-3.[Crossref] Zbl1276.46063
  20. Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  21. Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. 
  22. Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  23. Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004. 
  24. Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  25. Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  26. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  27. Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  28. Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992. 

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