In this article, we first extend several basic theorems of the operation of vector in 3-dimensional Euclidean spaces. Then three unit vectors: e1, e2, e3 and the definition of vector function in the same spaces are introduced. By dint of unit vector the main operation properties as well as the differentiation formulas of vector function are shown [12].
@article{bwmeta1.element.doi-10_2478_v10037-010-0001-2,
author = {Xiquan Liang and Piqing Zhao and Ou Bai},
title = {Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {1-10},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0001-2}
}
Xiquan Liang; Piqing Zhao; Ou Bai. Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces. Formalized Mathematics, Tome 18 (2010) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0001-2/
[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. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 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] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
[7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
[8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
[9] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
[10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
[11] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
[12] Murray R. Spiegel. Vector Analysis and an Introduction to Tensor Analysis. McGraw-Hill Book Company, New York, 1959.
[13] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.