Second-Order Partial Differentiation of Real Binary Functions

• Autorzy: Bing Xie , Xiquan Liang , Xiuzhuan Shen
• Języki publikacji: EN

Abstrakty

EN

In this article we define second-order partial differentiation of real binary functions and discuss the relation of second-order partial derivatives and partial derivatives defined in [17].

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2009
• Tom: 17
• Numer: 2
• Strony: 79-87

Daty

wydano

2009-01-01

online

2009-07-14

Twórcy

autor

Bing Xie

• Qingdao University of Science and Technology, China

autor

Xiquan Liang

• Qingdao University of Science and Technology, China

autor

Xiuzhuan Shen

• Qingdao University of Science and Technology, China

Bibliografia

• [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [6] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
• [7] 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]
• [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
• [9] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
• [10] Jarosław Kotowicz. Properties of real functions. Formalized Mathematics, 1(4):781-786, 1990.
• [11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
• [12] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
• [13] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
• [14] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
• [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [16] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
• [17] 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.[Crossref]

Identyfikatory

DOI

10.2478/v10037-009-0009-7