BS IEC 60050-101-1999 International electrotechnical vocabulary - Mathematics《国际电工词汇 数学》.pdf

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1、BRITISH STANDARD BS IEC 60050-101: 1998 International Electrotechnical Vocabulary Part 101: Mathematics ICS 01.040.07; 01.040.29; 07.020; 29.020BSIEC60050-101:1998 This British Standard, having been prepared under the directionof the Electrotechnical Sector Committee, was publishedunder the authorit

2、y ofthe Standards Committee andcomes into effect on 15January1999 BSI 07-1999 ISBN 0 580 30988 6 National foreword This British Standard reproduces verbatim IEC60050-101:1998 and implements it as the UK national standard. It partially supersedes BS4727-1:Group 1:1983 The UK participation in its prep

3、aration was entrusted to Technical Committee GEL/1, Terminology, which has the responsibility to: aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; monito

4、r related international and European developments and promulgate them in the UK. A list of organizations represented on this committee can be obtained on request to its secretary. From 1January 1997, all IEC publications have the number60000 added to the old number. For instance, IEC 27-1 has been r

5、enumbered as IEC60027-1. For a period of time during the change over from one numbering system to the other, publications may contain identifiers from both systems. Cross-references The British Standards which implement international or European publications referred to in this document may be found

6、 in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards

7、are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, theCEI IEC title page, page ii, pages 1 to116 and a back cover.

8、This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. Amendments issued since publication Amd. No. Date CommentsBSIEC60050-101:1998 BSI 07-1999 i Contents Page National foreword Inside fr

9、ont cover Text of CEI IEC 60050-101 1ii blankBSIEC60050-101:1998 ii BSI 07-1999 Contents Page Introduction 1 Normative references 1 Section 101-11. Scalar and vector quantities 3 Section 101-12. Concepts related to information 26 Section 101-13. Distributions and integral transformations 29 Section

10、101-14. Quantities dependent on a variable 36 Section 101-15. Waves 69 List of letter symbols 79 List of mathematical signs 80 Index 81BSIEC60050-101:1998 BSI 07-1999 1 Introduction Part 101 deals only with some fields of mathematics which are particularly useful for IEV. According to the case, the

11、chosen point of view is mathematically or physically oriented. The definitions of mathematical concepts are not intended to be complete mathematical definitions, but are given for identification and terminology. The letter symbols and mathematical signs are given for information only. The relevant i

12、nternational standards are IEC60027 and ISO31. Normative references IEC 60027-1:1992, Letter symbols to be used in electrical technology Part 1: General. IEC 60050(161):1990, International Electrotechnical Vocabulary Chapter 161: Electromagnetic compatibility. IEC 60050(701):1988, International Elec

13、trotechnical Vocabulary Chapter 701: Telecommunications, channels and networks. IEC 60050(702):1992, International Electrotechnical Vocabulary Chapter 702: Oscillations, signals and related devices. IEC 60050(705):1995, International Electrotechnical Vocabulary Chapter 705: Radio wave propagation. I

14、SO 31-11:1992, Quantities and units Part 11: Mathematical signs and symbols for use in the physical sciences and technology. ISO/IEC 2382-1:1993, Information Technology Vocabulary Part 1: Fundamental terms. ISO 3534-1:1993, Statistics Vocabulary and symbols Part 1: Probability and general statistica

15、l terms. 2 blankBSIEC60050-101:1998 BSI 07-1999 3 Section 101-11. Scalar and vector quantities 101-11-01 valeur absolue Pour un nombre rel a, le nombre non ngatif, soit a soit a. NOTE 1La valeur absolue de a est reprsente par; abs a est aussi utilis. NOTE 2La notion de valeur absolue peut sappliquer

16、 une grandeur scalaire relle. absolute value For a real number a, the non-negative number, either a or a. NOTE 1The absolute value of a is denoted by; abs a is also used. NOTE 2The concept of absolute value may be applied to a real scalar quantity. 101-11-02 nombre complexe Couple ordonn de nombres

17、rels, a et b, gnralement reprsent par c = a +jb o lunit imaginaire j vrifie j 2 =1. NOTE 1Un nombre complexe peat aussi tre reprsent par c = (cos +j sin )= e joest un nombre rel non ngatif et un nombre rel. NOTE 2En lectrotechnique, le symbole j est prfr au symbole i, usuel en mathmatiques. NOTE 3En

18、 lectrotechnique, un nombre complexe peut tre reprsent par un symbole littral soulign, par exemple: c. complex number Ordered pair of real numbers a and b, usually denoted by c =a+jb where the imaginary unit j satisfies j 2 =1. NOTE 1A complex number may also be expressed as c=(cos +j sin ) = e jwhe

19、reis a non-negative real number and a real number. NOTE 2In electrotechnology, the symbol j is preferred to the symbol i, usual in mathematics. NOTE 3In electrotechnology, a complex number may be denoted by an underlined letter symbol, for example:c. a a c c c c c cBSIEC60050-101:1998 4 BSI 07-1999

20、101-11-03 partie relle Composante a dun nombre complexe c = a+jb. NOTE 1La partie relle dun nombre complexe c est reprsente par Re c ou par c. NOTE 2La notion de partie relle peut sappliquer une grandeur scalaire, vectorielle ou tensorielle complexe et une matrice dlments complexes. real part The pa

21、rt a of a complex number c = a +jb. NOTE 1The real part of a complex number c is denoted by Re c or by c. NOTE 2The concept of real part may be applied to a complex scalar, vector or tensor quantity or to a matrix of complex elements. 101-11-04 partie imaginaire Composante b dun nombre complexe c =

22、a +jb. NOTE 1La partie imaginaire dun nombre complexe c est reprsente par Im c ou par c . NOTE 2La notion de partie imaginaire peut sappliquer une grandeur scalaire, vectorielle ou tensorielle complexe et une matrice dlments complexes. imaginary part The part b of a complex number c = a+jb. NOTE 1Th

23、e imaginary part of a complex number c is denoted by Im c or by c . NOTE 2The concept of imaginary part may be applied to a complex scalar, vector or tensor quantity or to a matrix of complex elements. 101-11-05 conjugu Nombre complexe c*=a jb associ au nombre complexe c = a+jb. NOTE 1La conjugu du

24、nombre complexe c = e jest c*= e j . NOTE 2La notion de conjugu peut sappliquer une grandeur scalaire, vectorielle ou tensorielle complexe et une matrice dlments complexes. conjugate Complex number c*=ajb associated with the complex number c = a+jb. NOTE 1The conjugate of the complex number c = e ji

25、s c*= e j . NOTE 2The concept of conjugate may be applied to a complex scalar, vector or tensor quantity or to a matrix of complex elements. c c c cBSIEC60050-101:1998 BSI 07-1999 5 101-11-06 racine carre Nombre dont le produit par lui-mme est gal un nombre rel ou complexe donn. NOTETout nombre rel

26、ou complexe non nul a deux racines carres, qui sont des nombres opposs. Pour un nombre rel positif a, la racine carre positive est reprsente par a ouet la racine carre ngative para ou. square root Number for which the product by itself is equal to a given real or complex number. NOTEEvery non-zero r

27、eal or complex number has two square roots, each being the negative of the other. For a positive real number a, the positive square root is denoted by a orand the negative square root bya or. 101-11-07 module Nombre rel non-ngatif dont le carr est gal au produit dun nombre complexe c = a +jb par son

28、 conjugu: NOTELa notion de module peut sappliquer une grandeur scalaire complexe. modulus Non-negative real number, the square of which is equal to the product of a complex number c = a+jb and its conjugate: NOTEThe concept of modulus may be applied to a complex scalar quantity. a a a a c ccc* a 2 b

29、 2 + = c ccc* a 2 b 2 + =BSIEC60050-101:1998 6 BSI 07-1999 101-11-08 argument (symbole: arg) Nombre rel tel que;0 si a 0 si a =0, b 0 if a 0 if a =0, b 0 where;/2arctan x ;/2 according to ISO31-11. NOTE 2The concept of argument may be applied to a complex scalar quantity. 101-11-09 grandeur scalaire

30、 scalaire (nom masculin) Grandeur pour laquelle la valeur numrique est un nombre rel ou complexe unique. NOTEDans un espace tridimensionnel o la notion de direction est dfinie, le terme grandeur scalaire est souvent restreint une grandeur indpendante de la direction. scalar (quantity) Quantity the n

31、umerical value of which is a single real or complex number. NOTEIn a three-dimensional space where the concept of direction is defined, the term “scalar quantity” is often restricted to a quantity independent of direction. c cBSIEC60050-101:1998 BSI 07-1999 7 101-11-10 grandeur vectorielle vecteur G

32、randeur reprsentable par un lment dun ensemble, dans lequel le produit dun lment quelconque par un nombre soit rel soit complexe, ainsi que la somme de deux lments quelconques sont des lments de lensemble. NOTE 1Une grandeur vectorielle dans un espace n dimensions est caractrise par un ensemble ordo

33、nn de n nombres rels ou complexes, qui dpendent du choix des n vecteurs de base si n est suprieur 1. NOTE 2Dans un espace rel deux ou trois dimensions, une grandeur vectorielle est reprsentable par un segment orient caractris par sa direction et sa longueur. NOTE 3Une grandeur vectorielle complexe V

34、 est dfinie par une partie relle et une partie imaginaire: V = A +jB o A et B sont des grandeurs vectorielles relles. NOTE 4Une grandeur vectorielle est reprsente par un symbole littral en gras ou par un symbole surmont dune flche: V ou. vector (quantity) Quantity which can be represented as an elem

35、ent of a set, in which both the product of any element and either any real or any complex number and also the sum of any two elements are elements of the set. NOTE 1A vector quantity in an n-dimensional space is characterized by an ordered set of n real or complex numbers, which depend on the choice

36、 of the n base vectors if n is greater than1. NOTE 2For a real two- or three-dimensional space, a vector quantity can be represented as an oriented line segment characterized by its direction and length. NOTE 3A complex vector quantity V is defined by a real part and an imaginary part: V = A +jB whe

37、re A and B are real vector quantities. NOTE 4A vector quantity is indicated by a letter symbol in bold-face type or by an arrow above a letter symbol: V or. 101-11-11 matrice Ensemble ordonn de m n lments, reprsent par un tableau de m lignes et n colonnes. NOTELes lments peuvent tre des nombres, des

38、 grandeurs scalaires, vectorielles ou tensorielles, des ensembles, des fonctions, des oprateurs ou mme des matrices. matrix Ordered set of m n elements represented by m rows and n columns. NOTEThe elements may be numbers, scalar, vector or tensor quantities, sets, functions, operators or even matric

39、es. V VBSIEC60050-101:1998 8 BSI 07-1999 101-11-12 grandeur tensorielle (du second ordre) tenseur (du second ordre) Grandeur reprsentable dans un espace n dimensions par une matrice carre de n n grandeurs relles ou complexest ij , qui dcrit une transformation linaire dun vecteur A en un vecteur B: B

40、 i =C j t ij A j tensor (quantity) (of second order) Quantity characterized in an n-dimensional space by an n n square matrix of real or complex quantities t ij , which describes a linear transformation of a vector A into a vector B: B i =C j t ij A j . 101-11-13 vecteur de base Dans un espace n dim

41、ensions, chacun des lments dun ensemble de n grandeurs vectorielles linairement indpendantes. NOTE 1Pour un ensemble donn de vecteurs de base A 1 , A 2 , . A n , toute grandeur vectorielle V peut tre exprime de faon univoque comme une combinaison linaire. V = a 1 A 1 + a 2 A 2 +.+a n A n o a 1 , a 2

42、 , . a nsont des grandeurs dont chacune a pour valeur numrique un nombre rel ou complexe unique. NOTE 2On choisit gnralement comme vecteurs de base, dnots e 1 , e 2 , .e n , des grandeurs vectorielles relles orthonormes sans dimension. NOTE 3Dans un espace trois dimensions, les vecteurs de base sont

43、 gnralement choisis par convention de faon former un tridre direct. Ils peuvent tre dnots e x , e y , e z , ou i, j, k. base vector In an n-dimensional space, one of a set of n linearly independent vector quantities. NOTE 1For a given set of base vectors A 1 , A 2 , . A n , any vector quantity V can

44、 be uniquely expressed as a linear combination V = a 1 A 1 + a 2 A 2 +.+a n A n where a 1 , a 2 , .a nare quantities, the numerical value of each being a single real or complex number. NOTE 2The base vectors are generally chosen as real orthonormal vector quantities of dimension one, denoted e 1 , e

45、 2 , . e n . NOTE 3In a three-dimensional space, the base vectors are usually taken by convention to form a right-handed trihedron. They can be denoted e x , e y , e z , or i, j, k.BSIEC60050-101:1998 BSI 07-1999 9 101-11-14 coordonne (dun vecteur) Chacune des n quantits a 1 , a 2 , . a ncaractrisan

46、t la grandeur vectorielle V = a 1 A 1 + a 2 A 2 +.+a n A n o A 1 , A 2 , . A n , sont les vecteurs de base. NOTEEn anglais, le terme coordinate est employ uniquement pour les coordonnes dun vecteur de position. component (of a vector) coordinate (of a vector) Any of the n quantities a 1 , a 2 , . a

47、ncharacterizing the vector quantity V = a 1 A 1 + a 2 A 2 +.+a n A n where A 1 , A 2 , . A n , are the base vectors. NOTEIn English, the term “coordinate” is only used for the components of a position vector. 101-11-15 composante (dun vecteur) Chacun des lments dun ensemble de grandeurs vectorielles

48、 linairement indpendantes dont la somme est gale une grandeur vectorielle donne. NOTEExemple: chacun des produits dune coordonne dune grandeur vectorielle par le vecteur de base correspondant. component vector (of a vector) One of a set of linearly independent vector quantities, the sum of which is equal to a given vector quantity. NOTEExample: any of the products of a component of a vector quantity and the corresponding base vector. 101-11-16 somme (vectorielle) Grandeur vectorielle dont chaque coordonne est la somme des coordonnes correspondantes de grandeu