Functions of Several Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1977
|
| Ausgabe: | 2nd Edition |
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this book is to give a systematic development of differential and integral calculus for functions of several variables. The traditional topics from advanced calculus are included: maxima and minima, chain rule, implicit function theorem, multiple integrals, divergence and Stokes's theorems, and so on. However, the treatment differs in several important respects from the traditional one. Vector notation is used throughout, and the distinction is maintained between n-dimensional euclidean space En and its dual. The elements of the Lebesgue theory of integrals are given. In place of the traditional vector analysis in £3, we introduce exterior algebra and the calculus of exterior differential forms. The formulas of vector analysis then become special cases of formulas about differential forms and integrals over manifolds lying in P. The book is suitable for a one-year course at the advanced undergraduate level. By omitting certain chapters, a one semester course can be based on it. For instance, if the students already have a good knowledge of partial differentiation and the elementary topology of P, then substantial parts of Chapters 4, 5, 7, and 8 can be covered in a semester. Some knowledge of linear algebra is presumed. However, results from linear algebra are reviewed as needed (in some cases without proof). A number of changes have been made in the first edition. Many of these were suggested by classroom experience. A new Chapter 2 on elementary topology has been added |
| Beschreibung: | 1 Online-Ressource (XII, 412 p) |
| ISBN: | 9781468494617 9781468494631 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4684-9461-7 |
Internformat
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Datensatz im Suchindex
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| author | Fleming, Wendell |
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| building | Verbundindex |
| bvnumber | BV042421226 |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9461-7 |
| edition | 2nd Edition |
| format | Electronic eBook |
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| id | DE-604.BV042421226 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468494617 9781468494631 |
| issn | 0172-6056 |
| language | English |
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| spelling | Fleming, Wendell Verfasser aut Functions of Several Variables by Wendell Fleming 2nd Edition New York, NY Springer New York 1977 1 Online-Ressource (XII, 412 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 The purpose of this book is to give a systematic development of differential and integral calculus for functions of several variables. The traditional topics from advanced calculus are included: maxima and minima, chain rule, implicit function theorem, multiple integrals, divergence and Stokes's theorems, and so on. However, the treatment differs in several important respects from the traditional one. Vector notation is used throughout, and the distinction is maintained between n-dimensional euclidean space En and its dual. The elements of the Lebesgue theory of integrals are given. In place of the traditional vector analysis in £3, we introduce exterior algebra and the calculus of exterior differential forms. The formulas of vector analysis then become special cases of formulas about differential forms and integrals over manifolds lying in P. The book is suitable for a one-year course at the advanced undergraduate level. By omitting certain chapters, a one semester course can be based on it. For instance, if the students already have a good knowledge of partial differentiation and the elementary topology of P, then substantial parts of Chapters 4, 5, 7, and 8 can be covered in a semester. Some knowledge of linear algebra is presumed. However, results from linear algebra are reviewed as needed (in some cases without proof). A number of changes have been made in the first edition. Many of these were suggested by classroom experience. A new Chapter 2 on elementary topology has been added Mathematics Mathematics, general Mathematik Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Mehrere reelle Variable (DE-588)4202599-0 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktion (DE-588)4195664-3 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Infinitesimalrechnung (DE-588)4072798-1 s 2\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 3\p DE-604 Funktion (DE-588)4195664-3 s 4\p DE-604 Reelle Funktion (DE-588)4048918-8 s 5\p DE-604 Mehrere reelle Variable (DE-588)4202599-0 s 6\p DE-604 https://doi.org/10.1007/978-1-4684-9461-7 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 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fleming, Wendell Functions of Several Variables Mathematics Mathematics, general Mathematik Analysis (DE-588)4001865-9 gnd Reelle Funktion (DE-588)4048918-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktion (DE-588)4195664-3 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4048918-8 (DE-588)4277015-4 (DE-588)4202599-0 (DE-588)4071510-3 (DE-588)4195664-3 (DE-588)4072798-1 |
| title | Functions of Several Variables |
| title_auth | Functions of Several Variables |
| title_exact_search | Functions of Several Variables |
| title_full | Functions of Several Variables by Wendell Fleming |
| title_fullStr | Functions of Several Variables by Wendell Fleming |
| title_full_unstemmed | Functions of Several Variables by Wendell Fleming |
| title_short | Functions of Several Variables |
| title_sort | functions of several variables |
| topic | Mathematics Mathematics, general Mathematik Analysis (DE-588)4001865-9 gnd Reelle Funktion (DE-588)4048918-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktion (DE-588)4195664-3 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Analysis Reelle Funktion Mehrere Variable Mehrere reelle Variable Funktion Mathematik Funktion Infinitesimalrechnung |
| url | https://doi.org/10.1007/978-1-4684-9461-7 |
| work_keys_str_mv | AT flemingwendell functionsofseveralvariables |