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

Xiquan Liang; Piqing Zhao; Ou Bai

Formalized Mathematics (2010)

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

Abstract

top
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

top

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

top
  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 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] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  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. 

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.