Multivariable Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1984
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its derivatives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case |
| Beschreibung: | 1 Online-Ressource (XIV, 656 p) |
| ISBN: | 9781461252283 9781461297475 |
| DOI: | 10.1007/978-1-4612-5228-3 |
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| 500 | |a This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its derivatives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case | ||
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Datensatz im Suchindex
| _version_ | 1804153092212523008 |
|---|---|
| any_adam_object | |
| author | Price, G. Baley |
| author_facet | Price, G. Baley |
| author_role | aut |
| author_sort | Price, G. Baley |
| author_variant | g b p gb gbp |
| building | Verbundindex |
| bvnumber | BV042420373 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863766829 (DE-599)BVBBV042420373 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-5228-3 |
| format | Electronic eBook |
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| id | DE-604.BV042420373 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461252283 9781461297475 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855790 |
| oclc_num | 863766829 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIV, 656 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer New York |
| record_format | marc |
| spelling | Price, G. Baley Verfasser aut Multivariable Analysis by G. Baley Price New York, NY Springer New York 1984 1 Online-Ressource (XIV, 656 p) txt rdacontent c rdamedia cr rdacarrier This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its derivatives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case Mathematics Real Functions Mathematik Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Differentialrechnung (DE-588)4012252-9 s 2\p DE-604 Funktionentheorie (DE-588)4018935-1 s 3\p DE-604 Integralrechnung (DE-588)4027232-1 s 4\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 5\p DE-604 https://doi.org/10.1007/978-1-4612-5228-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Price, G. Baley Multivariable Analysis Mathematics Real Functions Mathematik Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Differentialrechnung (DE-588)4012252-9 gnd Integralrechnung (DE-588)4027232-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4018935-1 (DE-588)4040708-1 (DE-588)4012252-9 (DE-588)4027232-1 (DE-588)4001865-9 |
| title | Multivariable Analysis |
| title_auth | Multivariable Analysis |
| title_exact_search | Multivariable Analysis |
| title_full | Multivariable Analysis by G. Baley Price |
| title_fullStr | Multivariable Analysis by G. Baley Price |
| title_full_unstemmed | Multivariable Analysis by G. Baley Price |
| title_short | Multivariable Analysis |
| title_sort | multivariable analysis |
| topic | Mathematics Real Functions Mathematik Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd Differentialrechnung (DE-588)4012252-9 gnd Integralrechnung (DE-588)4027232-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematics Real Functions Mathematik Mehrere Variable Funktionentheorie Multivariate Analyse Differentialrechnung Integralrechnung Analysis |
| url | https://doi.org/10.1007/978-1-4612-5228-3 |
| work_keys_str_mv | AT pricegbaley multivariableanalysis |