# Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces

Formalized Mathematics (2010)

• Volume: 18, Issue: 1, page 1-10
• ISSN: 1426-2630

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## Abstract

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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].

## How to cite

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Xiquan Liang, Piqing Zhao, and Ou Bai. "Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces." Formalized Mathematics 18.1 (2010): 1-10. <http://eudml.org/doc/266734>.

@article{XiquanLiang2010,
abstract = {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].},
author = {Xiquan Liang, Piqing Zhao, Ou Bai},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {1-10},
title = {Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces},
url = {http://eudml.org/doc/266734},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Xiquan Liang
AU - Piqing Zhao
AU - Ou Bai
TI - Vector Functions and their Differentiation Formulas in 3-dimensional Euclidean Spaces
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 1
EP - 10
AB - 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].
LA - eng
UR - http://eudml.org/doc/266734
ER -

## References

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9. [9] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
10. [10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
11. [11] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
12. [12] Murray R. Spiegel. Vector Analysis and an Introduction to Tensor Analysis. McGraw-Hill Book Company, New York, 1959.
13. [13] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.

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