Derivatives and Integrals of Multivariable Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2003
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text is appropriate for a one-semester course in what is usually called advanced calculus of several variables. The approach taken here extends elementary results about derivatives and integrals of single-variable functions to functions in several-variable Euclidean space. The elementary material in the single- and several-variable case leads naturally to significant advanced theorems about functions of multiple variables. In the first three chapters, differentiability and derivatives are defined; properties of derivatives reducible to the scalar, real-valued case are discussed; and two results from the vector case, important to the theoretical development of curves and surfaces, are presented. The next three chapters proceed analogously through the development of integration theory. Integrals and integrability are defined; properties of integrals of scalar functions are discussed; and results about scalar integrals of vector functions are presented. The development of these latter theorems, the vector-field theorems, brings together a number of results from other chapters and emphasizes the physical applications of the theory |
| Beschreibung: | 1 Online-Ressource (X, 319p. 41 illus) |
| ISBN: | 9781461200352 9780817642747 |
| DOI: | 10.1007/978-1-4612-0035-2 |
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| 500 | |a This text is appropriate for a one-semester course in what is usually called advanced calculus of several variables. The approach taken here extends elementary results about derivatives and integrals of single-variable functions to functions in several-variable Euclidean space. The elementary material in the single- and several-variable case leads naturally to significant advanced theorems about functions of multiple variables. In the first three chapters, differentiability and derivatives are defined; properties of derivatives reducible to the scalar, real-valued case are discussed; and two results from the vector case, important to the theoretical development of curves and surfaces, are presented. The next three chapters proceed analogously through the development of integration theory. Integrals and integrability are defined; properties of integrals of scalar functions are discussed; and results about scalar integrals of vector functions are presented. The development of these latter theorems, the vector-field theorems, brings together a number of results from other chapters and emphasizes the physical applications of the theory | ||
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Datensatz im Suchindex
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| author | Guzman, Alberto |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0035-2 |
| format | Electronic eBook |
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| id | DE-604.BV042419413 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461200352 9780817642747 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854830 |
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| physical | 1 Online-Ressource (X, 319p. 41 illus) |
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| publishDate | 2003 |
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| publisher | Birkhäuser Boston |
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| spelling | Guzman, Alberto Verfasser aut Derivatives and Integrals of Multivariable Functions by Alberto Guzman Boston, MA Birkhäuser Boston 2003 1 Online-Ressource (X, 319p. 41 illus) txt rdacontent c rdamedia cr rdacarrier This text is appropriate for a one-semester course in what is usually called advanced calculus of several variables. The approach taken here extends elementary results about derivatives and integrals of single-variable functions to functions in several-variable Euclidean space. The elementary material in the single- and several-variable case leads naturally to significant advanced theorems about functions of multiple variables. In the first three chapters, differentiability and derivatives are defined; properties of derivatives reducible to the scalar, real-valued case are discussed; and two results from the vector case, important to the theoretical development of curves and surfaces, are presented. The next three chapters proceed analogously through the development of integration theory. Integrals and integrability are defined; properties of integrals of scalar functions are discussed; and results about scalar integrals of vector functions are presented. The development of these latter theorems, the vector-field theorems, brings together a number of results from other chapters and emphasizes the physical applications of the theory Mathematics Global analysis (Mathematics) Global analysis Real Functions Analysis Global Analysis and Analysis on Manifolds Measure and Integration Mathematik Mehrere Variable (DE-588)4277015-4 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 https://doi.org/10.1007/978-1-4612-0035-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Guzman, Alberto Derivatives and Integrals of Multivariable Functions Mathematics Global analysis (Mathematics) Global analysis Real Functions Analysis Global Analysis and Analysis on Manifolds Measure and Integration Mathematik Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4001865-9 |
| title | Derivatives and Integrals of Multivariable Functions |
| title_auth | Derivatives and Integrals of Multivariable Functions |
| title_exact_search | Derivatives and Integrals of Multivariable Functions |
| title_full | Derivatives and Integrals of Multivariable Functions by Alberto Guzman |
| title_fullStr | Derivatives and Integrals of Multivariable Functions by Alberto Guzman |
| title_full_unstemmed | Derivatives and Integrals of Multivariable Functions by Alberto Guzman |
| title_short | Derivatives and Integrals of Multivariable Functions |
| title_sort | derivatives and integrals of multivariable functions |
| topic | Mathematics Global analysis (Mathematics) Global analysis Real Functions Analysis Global Analysis and Analysis on Manifolds Measure and Integration Mathematik Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Global analysis Real Functions Analysis Global Analysis and Analysis on Manifolds Measure and Integration Mathematik Mehrere Variable |
| url | https://doi.org/10.1007/978-1-4612-0035-2 |
| work_keys_str_mv | AT guzmanalberto derivativesandintegralsofmultivariablefunctions |