| 000 | 07068cam a2200613Ia 4500 | ||
|---|---|---|---|
| 001 | ocn162579274 | ||
| 003 | OCoLC | ||
| 005 | 20141103172225.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 070806s2002 ne a ob 001 0 eng d | ||
| 040 |
_aOPELS _beng _cOPELS _dOPELS _dOCLCQ _dN$T _dYDXCP _dMERUC _dE7B _dIDEBK _dTULIB _dOCLCO _dOCLCQ _dOPELS _dOCLCF _dDEBBG |
||
| 019 |
_a176877101 _a441810141 _a647652809 _a779919574 |
||
| 020 | _a9780444511232 | ||
| 020 | _a0444511237 | ||
| 020 | _a9780080529585 (electronic bk.) | ||
| 020 | _a0080529585 (electronic bk.) | ||
| 029 | 1 |
_aNZ1 _b12433563 |
|
| 029 | 1 |
_aAU@ _b000048130309 |
|
| 029 | 1 |
_aDEBBG _bBV039830196 |
|
| 029 | 1 |
_aNZ1 _b15192888 |
|
| 029 | 1 |
_aDEBBG _bBV036962328 |
|
| 035 |
_a(OCoLC)162579274 _z(OCoLC)176877101 _z(OCoLC)441810141 _z(OCoLC)647652809 _z(OCoLC)779919574 |
||
| 037 |
_a126897:128764 _bElsevier Science & Technology _nhttp://www.sciencedirect.com |
||
| 050 | 4 |
_aQA255 _b.O37 2002eb |
|
| 072 | 7 |
_aQA _2lcco |
|
| 072 | 7 |
_aMAT _x002040 _2bisacsh |
|
| 082 | 0 | 4 |
_a512 _222 |
| 049 | _aTEFA | ||
| 100 | 1 | _aOlariu, Silviu. | |
| 245 | 1 | 0 |
_aComplex numbers in N dimensions _h[electronic resource] / _cSilviu Olariu. |
| 250 | _a1st ed. | ||
| 260 |
_aAmsterdam ; _aBoston : _bElsevier, _c2002. |
||
| 300 |
_a1 online resource (xv, 269 p.) : _bill. |
||
| 490 | 1 |
_aNorth-Holland mathematics studies, _x0304-0208 ; _v190 |
|
| 520 | _aTwo 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 | _aIncludes bibliographical references (p. 261) and index. | ||
| 588 | _aDescription based on print version record. | ||
| 505 | 0 | _aCover -- 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 | _aNumbers, Complex. | |
| 650 | 7 |
_aMATHEMATICS _xAlgebra _xIntermediate. _2bisacsh |
|
| 650 | 7 |
_aNumbers, Complex. _2fast _0(OCoLC)fst01041230 |
|
| 655 | 4 | _aElectronic books. | |
| 776 | 0 | 8 |
_iPrint version: _aOlariu, Silviu. _tComplex numbers in N dimensions. _b1st ed. _dAmsterdam ; Boston : Elsevier, 2002 _z0444511237 _z9780444511232 _w(DLC) 2002070015 _w(OCoLC)49704592 |
| 830 | 0 |
_aNorth-Holland mathematics studies ; _v190. _x0304-0208 |
|
| 856 | 4 | 0 |
_3ScienceDirect _uhttp://www.sciencedirect.com/science/book/9780444511232 |
| 856 | 4 |
_uhttp://www.sciencedirect.com/science/publication?issn=03040208&volume=190 _3Volltext |
|
| 938 |
_aYBP Library Services _bYANK _n2722172 |
||
| 938 |
_aebrary _bEBRY _nebr10190865 |
||
| 938 |
_aIngram Digital eBook Collection _bIDEB _n105479 |
||
| 938 |
_aEBSCOhost _bEBSC _n207217 |
||
| 942 | _cEB | ||
| 994 |
_aC0 _bTEF |
||
| 999 |
_c21826 _d21826 |
||