Continuous Functions of Vector Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2002
|
| 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 focus is on expanding the concept of continuity; specifically, we establish theorems related to extreme and intermediate values, generalizing the important results regarding continuous functions of one real variable. We begin by considering the function f(x, y, ... ) of multiple variables as a function of the single vector variable (x, y, ... ). It turns out that most of the n treatment does not need to be limited to the finite-dimensional spaces R , so we will often place ourselves in an arbitrary vector space equipped with the right tools of measurement. We then proceed much as one does with functions on R. First we give an algebraic and metric structure to the set of vectors. We then define limits, leading to the concept of continuity and to properties of continuous functions. Finally, we enlarge upon some topological concepts that surface along the way. A thorough understanding of single-variable calculus is a fundamental requirement. The student should be familiar with the axioms of the real number system and be able to use them to develop elementary calculus, that is, to define continuous junction, derivative, and integral, and to prove their most important elementary properties. Familiarity with these properties is a must. To help the reader, we provide references for the needed theorems |
| Beschreibung: | 1 Online-Ressource (X, 207p. 26 illus) |
| ISBN: | 9781461200833 9780817642730 |
| DOI: | 10.1007/978-1-4612-0083-3 |
Internformat
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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 focus is on expanding the concept of continuity; specifically, we establish theorems related to extreme and intermediate values, generalizing the important results regarding continuous functions of one real variable. We begin by considering the function f(x, y, ... ) of multiple variables as a function of the single vector variable (x, y, ... ). It turns out that most of the n treatment does not need to be limited to the finite-dimensional spaces R , so we will often place ourselves in an arbitrary vector space equipped with the right tools of measurement. We then proceed much as one does with functions on R. First we give an algebraic and metric structure to the set of vectors. We then define limits, leading to the concept of continuity and to properties of continuous functions. Finally, we enlarge upon some topological concepts that surface along the way. A thorough understanding of single-variable calculus is a fundamental requirement. The student should be familiar with the axioms of the real number system and be able to use them to develop elementary calculus, that is, to define continuous junction, derivative, and integral, and to prove their most important elementary properties. Familiarity with these properties is a must. To help the reader, we provide references for the needed theorems | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Guzman, Alberto |
| author_facet | Guzman, Alberto |
| author_role | aut |
| author_sort | Guzman, Alberto |
| author_variant | a g ag |
| building | Verbundindex |
| bvnumber | BV042419430 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863670005 (DE-599)BVBBV042419430 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0083-3 |
| format | Electronic eBook |
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| isbn | 9781461200833 9780817642730 |
| language | English |
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| spelling | Guzman, Alberto Verfasser aut Continuous Functions of Vector Variables by Alberto Guzman Boston, MA Birkhäuser Boston 2002 1 Online-Ressource (X, 207p. 26 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 focus is on expanding the concept of continuity; specifically, we establish theorems related to extreme and intermediate values, generalizing the important results regarding continuous functions of one real variable. We begin by considering the function f(x, y, ... ) of multiple variables as a function of the single vector variable (x, y, ... ). It turns out that most of the n treatment does not need to be limited to the finite-dimensional spaces R , so we will often place ourselves in an arbitrary vector space equipped with the right tools of measurement. We then proceed much as one does with functions on R. First we give an algebraic and metric structure to the set of vectors. We then define limits, leading to the concept of continuity and to properties of continuous functions. Finally, we enlarge upon some topological concepts that surface along the way. A thorough understanding of single-variable calculus is a fundamental requirement. The student should be familiar with the axioms of the real number system and be able to use them to develop elementary calculus, that is, to define continuous junction, derivative, and integral, and to prove their most important elementary properties. Familiarity with these properties is a must. To help the reader, we provide references for the needed theorems Mathematics Global analysis (Mathematics) Functional analysis Analysis Functional Analysis Mathematik Vektorraum (DE-588)4130622-3 gnd rswk-swf Mehrere reelle Variable (DE-588)4202599-0 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Stetige Funktion (DE-588)4183162-7 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 s Mehrere reelle Variable (DE-588)4202599-0 s Vektorraum (DE-588)4130622-3 s 1\p DE-604 Stetige Funktion (DE-588)4183162-7 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-0083-3 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 |
| spellingShingle | Guzman, Alberto Continuous Functions of Vector Variables Mathematics Global analysis (Mathematics) Functional analysis Analysis Functional Analysis Mathematik Vektorraum (DE-588)4130622-3 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Funktion Mathematik (DE-588)4071510-3 gnd Stetige Funktion (DE-588)4183162-7 gnd |
| subject_GND | (DE-588)4130622-3 (DE-588)4202599-0 (DE-588)4071510-3 (DE-588)4183162-7 |
| title | Continuous Functions of Vector Variables |
| title_auth | Continuous Functions of Vector Variables |
| title_exact_search | Continuous Functions of Vector Variables |
| title_full | Continuous Functions of Vector Variables by Alberto Guzman |
| title_fullStr | Continuous Functions of Vector Variables by Alberto Guzman |
| title_full_unstemmed | Continuous Functions of Vector Variables by Alberto Guzman |
| title_short | Continuous Functions of Vector Variables |
| title_sort | continuous functions of vector variables |
| topic | Mathematics Global analysis (Mathematics) Functional analysis Analysis Functional Analysis Mathematik Vektorraum (DE-588)4130622-3 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Funktion Mathematik (DE-588)4071510-3 gnd Stetige Funktion (DE-588)4183162-7 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Functional analysis Analysis Functional Analysis Mathematik Vektorraum Mehrere reelle Variable Funktion Mathematik Stetige Funktion |
| url | https://doi.org/10.1007/978-1-4612-0083-3 |
| work_keys_str_mv | AT guzmanalberto continuousfunctionsofvectorvariables |