Have a personal or library account? Click to login
Partial Differentiation of Real Ternary Functions Cover

Partial Differentiation of Real Ternary Functions

By: Takao Inoué,  Bing Xie and  Xiquan Liang  
Open Access
|Jan 2011

References

  1. [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  2. [2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  3. [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  4. [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  5. [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  6. [6] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  7. [7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  8. [8] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.10.2478/v10037-007-0008-5
  9. [9] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  10. [10] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
  11. [11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  12. [12] Xiquan Liang, Piqing Zhao, and Ou Bai. Vector functions and their differentiation formulas in 3-dimensional Euclidean spaces. Formalized Mathematics, 18(1):1-10, 2010, doi: 10.2478/v10037-010-0001-2.10.2478/v10037-010-0001-2
  13. [13] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
  14. [14] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
  15. [15] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  16. [16] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.
  17. [17] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
  18. [18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  19. [19] Bing Xie, Xiquan Liang, and Hongwei Li. Partial differentiation of real binary functions. Formalized Mathematics, 16(4):333-338, 2008, doi:10.2478/v10037-008-0041-z.10.2478/v10037-008-0041-z
DOI: https://doi.org/10.2478/v10037-010-0005-y | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 39 - 46
Published on: Jan 5, 2011
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2011 Takao Inoué, Bing Xie, Xiquan Liang, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 18 (2010): Issue 1 (March 2010)