Complex numbers in N dimensions (Record no. 21826)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 07068cam a2200613Ia 4500 |
| 001 - CONTROL NUMBER | |
| control field | ocn162579274 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20141103172225.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cn||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 070806s2002 ne a ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | |
| Language of cataloging | eng |
| Transcribing agency | OPELS |
| Modifying agency | OPELS |
| -- | OCLCQ |
| -- | N$T |
| -- | YDXCP |
| -- | MERUC |
| -- | E7B |
| -- | IDEBK |
| -- | TULIB |
| -- | OCLCO |
| -- | OCLCQ |
| -- | OPELS |
| -- | OCLCF |
| -- | DEBBG |
| 019 ## - | |
| -- | 176877101 |
| -- | 441810141 |
| -- | 647652809 |
| -- | 779919574 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780444511232 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0444511237 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780080529585 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0080529585 (electronic bk.) |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 12433563 |
| 029 1# - (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000048130309 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBBG |
| System control number | BV039830196 |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 15192888 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBBG |
| System control number | BV036962328 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)162579274 |
| Canceled/invalid control number | (OCoLC)176877101 |
| -- | (OCoLC)441810141 |
| -- | (OCoLC)647652809 |
| -- | (OCoLC)779919574 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 126897:128764 |
| Source of stock number/acquisition | Elsevier Science & Technology |
| Note | http://www.sciencedirect.com |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA255 |
| Item number | .O37 2002eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | QA |
| Source | lcco |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 002040 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512 |
| Edition number | 22 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | TEFA |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Olariu, Silviu. |
| 245 10 - TITLE STATEMENT | |
| Title | Complex numbers in N dimensions |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | Silviu Olariu. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | Amsterdam ; |
| -- | Boston : |
| Name of publisher, distributor, etc. | Elsevier, |
| Date of publication, distribution, etc. | 2002. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xv, 269 p.) : |
| Other physical details | ill. |
| 490 1# - SERIES STATEMENT | |
| Series statement | North-Holland mathematics studies, |
| International Standard Serial Number | 0304-0208 ; |
| Volume/sequential designation | 190 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions. In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible. The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references (p. 261) and index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on print version record. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Contents -- Chapter 1. Hyperbolic Complex Numbers in Two Dimensions -- 1.1 Operations with hyperbolic twocomplex numbers -- 1.2 Geometric representation of hyperbolictwocomplex numbers -- 1.3 Exponential and trigonometric forms of a twocomplex number -- 1.4 Elementary functions of a twocomplex variable -- 1.5 Twocomplex power series -- 1.6 Analytic functions of twocomplex variables -- 1.7 Integrals of twocomplex functions -- 1.8 Factorization of twocomplex polynomials -- 1.9 Representation of hyperbolic twocomplex numbers by irreducible matrices -- Chapter 2. Complex Numbers in Three Dimensions -- 2.1 Operations with tricomplex numbers -- 2.2 Geometric representation of tricomplex numbers -- 2.3 The tricomplex cosexponential functions -- 2.4 Exponential and trigonometric forms of tricomplex numbers -- 2.5 Elementary functions of a tricomplex variable -- 2.6 Tricomplex power series -- 2.7 Analytic functions of tricomplex variables -- 2.8 Integrals of tricomplex functions -- 2.9 Factorization of tricomplex polynomials -- 2.10 Representation of tricomplex numbers by irreducible matrices -- Chapter 3. Commutative Complex Numbers in Four Dimensions -- 3.1 Circular complex numbers in four dimensions -- 3.2 Hyperbolic complex numbers in four dimensions -- 3.3 Planar complex numbers in four dimensions -- 3.4 Polar complex numbers in four dimensions -- Chapter 4. Complex Numbers in 5 Dimensions -- 4.1 Operations with polar complex numbers in 5 dimensions -- 4.2 Geometric representation of polar complex numbers in 5 dimensions -- 4.3 The polar 5-dimensional cosexponential functions -- 4.4 Exponential and trigonometric forms of polar 5-complex numbers -- 4.5 Elementary functions of a polar 5-complex variable -- 4.6 Power series of 5-complex numbers -- 4.7 Analytic functions of a polar 5-complex variable -- 4.8 Integrals of polar 5-complex functions -- 4.9 Factorization of polar 5-complex polynomials -- 4.10 Representation of polar 5-complex numbers by irreducible matrices -- Chapter 5. Complex Numbers in 6 Dimensions -- 5.1 Polar complex numbers in 6 dimensions -- 5.2 Planar complex numbers in 6 dimensions -- Chapter 6. Commutative Complex Numbers in n Dimensions -- 6.1 Polar complex numbers in n dimensions -- 6.2 Planar complex numbers in even n dimensions -- Bibliography -- Index -- Last Page. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numbers, Complex. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Algebra |
| -- | Intermediate. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numbers, Complex. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst01041230 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Olariu, Silviu. |
| Title | Complex numbers in N dimensions. |
| Edition | 1st ed. |
| Place, publisher, and date of publication | Amsterdam ; Boston : Elsevier, 2002 |
| International Standard Book Number | 0444511237 |
| -- | 9780444511232 |
| Record control number | (DLC) 2002070015 |
| -- | (OCoLC)49704592 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | North-Holland mathematics studies ; |
| Volume number/sequential designation | 190. |
| International Standard Serial Number | 0304-0208 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | ScienceDirect |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/book/9780444511232">http://www.sciencedirect.com/science/book/9780444511232</a> |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/publication?issn=03040208&volume=190">http://www.sciencedirect.com/science/publication?issn=03040208&volume=190</a> |
| Materials specified | Volltext |
| 938 ## - | |
| -- | YBP Library Services |
| -- | YANK |
| -- | 2722172 |
| 938 ## - | |
| -- | ebrary |
| -- | EBRY |
| -- | ebr10190865 |
| 938 ## - | |
| -- | Ingram Digital eBook Collection |
| -- | IDEB |
| -- | 105479 |
| 938 ## - | |
| -- | EBSCOhost |
| -- | EBSC |
| -- | 207217 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E(electronic)-Books |
| 994 ## - | |
| -- | C0 |
| -- | TEF |
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