MARC details
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03581nam a22005415i 4500 |
| 001 - CONTROL NUMBER |
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978-1-4419-9875-0 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20180115171508.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
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120516s2012 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781441998750 |
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978-1-4419-9875-0 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4419-9875-0 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA299.6-433 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBK |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT034000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Burgin, Mark. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Hypernumbers and Extrafunctions |
| Medium |
[electronic resource] : |
| Remainder of title |
Extending the Classical Calculus / |
| Statement of responsibility, etc. |
by Mark Burgin. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York : |
| -- |
Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2012. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
VII, 160 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
SpringerBriefs in Mathematics, |
| International Standard Serial Number |
2191-8198 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
-1. Introduction: How mathematicians solve ”unsolvable” problems.-2. Hypernumbers(Definitions and typology,Algebraic properties,Topological properties).-3. Extrafunctions(Definitions and typology, Algebraic properties, Topological properties).-4. How to differentiate any real function (Approximations, Hyperdifferentiation).-5. How to integrate any continuous real function (Partitions and covers, Hyperintegration over finite intervals, Hyperintegration over infinite intervals). -6. Conclusion: New opportunities -- Appendix -- References. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
“Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Functional analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Partial differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Physics. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analysis. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Functional Analysis. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Partial Differential Equations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Measure and Integration. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical Methods in Physics. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9781441998743 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
SpringerBriefs in Mathematics, |
| International Standard Serial Number |
2191-8198 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-1-4419-9875-0">http://dx.doi.org/10.1007/978-1-4419-9875-0</a> |
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ZDB-2-SMA |