Nonstandard Asymptotic Analysis (Record no. 30912)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02990nam a22004695i 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783540478102 |
| -- | 978-3-540-47810-2 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.3 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Berg, Imme. |
| 245 10 - TITLE STATEMENT | |
| Title | Nonstandard Asymptotic Analysis |
| Statement of responsibility, etc | by Imme Berg. |
| 260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Berlin, Heidelberg : |
| Name of publisher | Springer Berlin Heidelberg, |
| Year of publication | 1987. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XII, 192 p. |
| Other physical details | online resource. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Four examples of nonstandard reasoning in asymptotics -- Asymptotic expressions for the remainders associated to expansions of type , where cn+p/cn ? c -- Asymptotic expressions for the remainders associated to expansions of type : Critical regions, uniform behaviour -- External sets -- Approximation lemma's -- Shadow expansions. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the theory are presented via concrete examples, with many numerical and graphic illustrations. N. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Logic, Symbolic and mathematical. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematical Logic and Foundations. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/BFb0077577 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg, |
| -- | 1987. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0075-8434 ; |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK1618 | http://dx.doi.org/10.1007/BFb0077577 | E-BOOKS |