Complex Function Differentiability

Chanapat Pacharapokin; Hiroshi Yamazaki; Yasunari Shidama; Yatsuka Nakamura

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 67-72
  • ISSN: 1426-2630

Abstract

top
For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.

How to cite

top

Chanapat Pacharapokin, et al. "Complex Function Differentiability." Formalized Mathematics 17.2 (2009): 67-72. <http://eudml.org/doc/266915>.

@article{ChanapatPacharapokin2009,
abstract = {For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.},
author = {Chanapat Pacharapokin, Hiroshi Yamazaki, Yasunari Shidama, Yatsuka Nakamura},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {67-72},
title = {Complex Function Differentiability},
url = {http://eudml.org/doc/266915},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Chanapat Pacharapokin
AU - Hiroshi Yamazaki
AU - Yasunari Shidama
AU - Yatsuka Nakamura
TI - Complex Function Differentiability
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 67
EP - 72
AB - For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.
LA - eng
UR - http://eudml.org/doc/266915
ER -

References

top
  1. [1] Agnieszka Banachowicz and Anna Winnicka. Complex sequences. Formalized Mathematics, 4(1):121-124, 1993. 
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  4. [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  5. [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  6. [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  7. [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  8. [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  9. [9] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  10. [10] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990. 
  11. [11] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990. 
  12. [12] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  13. [13] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex sequence and continuity of complex function. Formalized Mathematics, 9(1):185-190, 2001. Zbl0951.93523
  14. [14] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997. 
  15. [15] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997. 
  16. [16] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  17. [17] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  18. [18] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  19. [19] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.