A Guide to Real Variables /:
A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | Dolciani mathematical expositions.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize. |
| Beschreibung: | Title from publishers bibliographic system (viewed on 30 Jan 2012). |
| Beschreibung: | 1 online resource (1 online resource) |
| ISBN: | 9780883859162 0883859165 |
Internformat
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn775428962 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 111104s2012 enk o 001 0 eng d | ||
| 040 | |a COO |b eng |e pn |c COO |d N$T |d YDXCP |d OCLCQ |d OCLCF |d CAMBR |d JSTOR |d OCLCQ |d EBLCP |d DEBSZ |d OCLCQ |d ZCU |d MERUC |d BNG |d OCLCQ |d VTS |d AGLDB |d ICG |d OCLCQ |d STF |d DKC |d OCLCQ |d AJS |d OCLCO |d RDF |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 923220588 |a 929120456 |a 1011023462 | ||
| 020 | |a 9780883859162 |q (electronic bk.) | ||
| 020 | |a 0883859165 |q (electronic bk.) | ||
| 035 | |a (OCoLC)775428962 |z (OCoLC)923220588 |z (OCoLC)929120456 |z (OCoLC)1011023462 | ||
| 037 | |a 22573/ctt69tzn2 |b JSTOR | ||
| 050 | 4 | |a QA331.5 | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 082 | 7 | |a 515.8 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Krantz, Steven G. |q (Steven George), |d 1951- |1 https://id.oclc.org/worldcat/entity/E39PBJw8VQ7cxG48KCfPym3RKd |0 http://id.loc.gov/authorities/names/n81051364 | |
| 245 | 1 | 2 | |a A Guide to Real Variables / |c Steven G. Krantz. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource (1 online resource) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Dolciani Mathematical Expositions ; |v v. 38 | |
| 500 | |a Title from publishers bibliographic system (viewed on 30 Jan 2012). | ||
| 505 | 0 | |a Contents -- Preface -- 1 Basics -- 1.1 Sets -- 1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations on Functions -- 1.5 Number Systems -- 1.5.1 The Real Numbers -- 1.6 Countable and Uncountable Sets -- 2 Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The Definition and Convergence -- 2.1.2 The Cauchy Criterion -- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle -- 2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special Sequences -- 3 Series -- 3.1 Introduction to Series | |
| 505 | 8 | |a 3.1.1 The Definition and Convergence3.1.2 Partial Sums -- 3.2 Elementary Convergence Tests -- 3.2.1 The Comparison Test -- 3.2.2 The Cauchy Condensation Test -- 3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence -- 3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts -- 3.3.2 Abel�s Test -- 3.3.3 Absolute and Conditional Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other Representations for e -- 3.4.3 Sums of Powers | |
| 505 | 8 | |a 3.5 Operations on Series3.5.1 Sums and Scalar Products of Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy Product -- 4 The Topology of the Real Line -- 4.1 Open and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets -- 4.1.3 Characterization of Open and Closed Sets in Terms of Sequences -- 4.1.4 Further Properties of Open and Closed Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior Points and Isolated Points -- 4.2.2 Accumulation Points -- 4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction -- 4.4.2 The Heine-Borel Theorem | |
| 505 | 8 | |a 4.4.3 The Topological Characterization of Compactness4.5 The Cantor Set -- 4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity -- 4.7 Perfect Sets -- 5 Limits and the Continuity of Functions -- 5.1 Definitions and Basic Properties -- 5.1.1 Limits -- 5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of Limits -- 5.1.4 Properties of Limits -- 5.1.5 Characterization of Limits Using Sequences -- 5.2 Continuous Functions -- 5.2.1 Continuity at a Point -- 5.2.2 The Topological Approach to Continuity -- 5.3 Topological Properties and Continuity | |
| 505 | 8 | |a 5.3.1 The Image of a Function5.3.2 Uniform Continuity -- 5.3.3 Continuity and Connectedness -- 5.3.4 The Intermediate Value Property -- 5.4 Monotonicity and Classifying Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2 Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6 The Derivative -- 6.1 The Concept of Derivative -- 6.1.1 The Definition -- 6.1.2 Properties of the Derivative -- 6.1.3 The Weierstrass Nowhere Differentiable Function -- 6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and Applications -- 6.2.1 Local Maxima and Minima | |
| 520 | |a A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize. | ||
| 650 | 0 | |a Functions of real variables. |0 http://id.loc.gov/authorities/subjects/sh85052357 | |
| 650 | 6 | |a Fonctions de variables réelles. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Functions of real variables |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Krantz, Steven G. |t Guide to Real Variables. |d Washington : Mathematical Association of America, ©2014 |z 9780883853443 |
| 830 | 0 | |a Dolciani mathematical expositions. |0 http://id.loc.gov/authorities/names/n42009859 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274 |3 Volltext | |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL3330367 | ||
| 938 | |a EBSCOhost |b EBSC |n 450274 | ||
| 938 | |a YBP Library Services |b YANK |n 7349787 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn775428962 |
|---|---|
| _version_ | 1813903426784854016 |
| adam_text | |
| any_adam_object | |
| author | Krantz, Steven G. (Steven George), 1951- |
| author_GND | http://id.loc.gov/authorities/names/n81051364 |
| author_facet | Krantz, Steven G. (Steven George), 1951- |
| author_role | |
| author_sort | Krantz, Steven G. 1951- |
| author_variant | s g k sg sgk |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.5 |
| callnumber-search | QA331.5 |
| callnumber-sort | QA 3331.5 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Contents -- Preface -- 1 Basics -- 1.1 Sets -- 1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations on Functions -- 1.5 Number Systems -- 1.5.1 The Real Numbers -- 1.6 Countable and Uncountable Sets -- 2 Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The Definition and Convergence -- 2.1.2 The Cauchy Criterion -- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle -- 2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special Sequences -- 3 Series -- 3.1 Introduction to Series 3.1.1 The Definition and Convergence3.1.2 Partial Sums -- 3.2 Elementary Convergence Tests -- 3.2.1 The Comparison Test -- 3.2.2 The Cauchy Condensation Test -- 3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence -- 3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts -- 3.3.2 Abel�s Test -- 3.3.3 Absolute and Conditional Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other Representations for e -- 3.4.3 Sums of Powers 3.5 Operations on Series3.5.1 Sums and Scalar Products of Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy Product -- 4 The Topology of the Real Line -- 4.1 Open and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets -- 4.1.3 Characterization of Open and Closed Sets in Terms of Sequences -- 4.1.4 Further Properties of Open and Closed Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior Points and Isolated Points -- 4.2.2 Accumulation Points -- 4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction -- 4.4.2 The Heine-Borel Theorem 4.4.3 The Topological Characterization of Compactness4.5 The Cantor Set -- 4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity -- 4.7 Perfect Sets -- 5 Limits and the Continuity of Functions -- 5.1 Definitions and Basic Properties -- 5.1.1 Limits -- 5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of Limits -- 5.1.4 Properties of Limits -- 5.1.5 Characterization of Limits Using Sequences -- 5.2 Continuous Functions -- 5.2.1 Continuity at a Point -- 5.2.2 The Topological Approach to Continuity -- 5.3 Topological Properties and Continuity 5.3.1 The Image of a Function5.3.2 Uniform Continuity -- 5.3.3 Continuity and Connectedness -- 5.3.4 The Intermediate Value Property -- 5.4 Monotonicity and Classifying Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2 Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6 The Derivative -- 6.1 The Concept of Derivative -- 6.1.1 The Definition -- 6.1.2 Properties of the Derivative -- 6.1.3 The Weierstrass Nowhere Differentiable Function -- 6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and Applications -- 6.2.1 Local Maxima and Minima |
| ctrlnum | (OCoLC)775428962 |
| 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 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06363cam a2200565Mi 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn775428962</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |||||||||||</controlfield><controlfield tag="008">111104s2012 enk o 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">COO</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">COO</subfield><subfield code="d">N$T</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">CAMBR</subfield><subfield code="d">JSTOR</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">EBLCP</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">ZCU</subfield><subfield code="d">MERUC</subfield><subfield code="d">BNG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">AGLDB</subfield><subfield code="d">ICG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">STF</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">RDF</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">923220588</subfield><subfield code="a">929120456</subfield><subfield code="a">1011023462</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780883859162</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0883859165</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)775428962</subfield><subfield code="z">(OCoLC)923220588</subfield><subfield code="z">(OCoLC)929120456</subfield><subfield code="z">(OCoLC)1011023462</subfield></datafield><datafield tag="037" ind1=" " ind2=" "><subfield code="a">22573/ctt69tzn2</subfield><subfield code="b">JSTOR</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA331.5</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">005000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515.8</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krantz, Steven G.</subfield><subfield code="q">(Steven George),</subfield><subfield code="d">1951-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJw8VQ7cxG48KCfPym3RKd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n81051364</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A Guide to Real Variables /</subfield><subfield code="c">Steven G. Krantz.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2012.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (1 online resource)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Dolciani Mathematical Expositions ;</subfield><subfield code="v">v. 38</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publishers bibliographic system (viewed on 30 Jan 2012).</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Contents -- Preface -- 1 Basics -- 1.1 Sets -- 1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations on Functions -- 1.5 Number Systems -- 1.5.1 The Real Numbers -- 1.6 Countable and Uncountable Sets -- 2 Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The Definition and Convergence -- 2.1.2 The Cauchy Criterion -- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle -- 2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special Sequences -- 3 Series -- 3.1 Introduction to Series</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.1.1 The Definition and Convergence3.1.2 Partial Sums -- 3.2 Elementary Convergence Tests -- 3.2.1 The Comparison Test -- 3.2.2 The Cauchy Condensation Test -- 3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence -- 3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts -- 3.3.2 Abelâ€?s Test -- 3.3.3 Absolute and Conditional Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other Representations for e -- 3.4.3 Sums of Powers</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.5 Operations on Series3.5.1 Sums and Scalar Products of Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy Product -- 4 The Topology of the Real Line -- 4.1 Open and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets -- 4.1.3 Characterization of Open and Closed Sets in Terms of Sequences -- 4.1.4 Further Properties of Open and Closed Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior Points and Isolated Points -- 4.2.2 Accumulation Points -- 4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction -- 4.4.2 The Heine-Borel Theorem</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.4.3 The Topological Characterization of Compactness4.5 The Cantor Set -- 4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity -- 4.7 Perfect Sets -- 5 Limits and the Continuity of Functions -- 5.1 Definitions and Basic Properties -- 5.1.1 Limits -- 5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of Limits -- 5.1.4 Properties of Limits -- 5.1.5 Characterization of Limits Using Sequences -- 5.2 Continuous Functions -- 5.2.1 Continuity at a Point -- 5.2.2 The Topological Approach to Continuity -- 5.3 Topological Properties and Continuity</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.3.1 The Image of a Function5.3.2 Uniform Continuity -- 5.3.3 Continuity and Connectedness -- 5.3.4 The Intermediate Value Property -- 5.4 Monotonicity and Classifying Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2 Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6 The Derivative -- 6.1 The Concept of Derivative -- 6.1.1 The Definition -- 6.1.2 Properties of the Derivative -- 6.1.3 The Weierstrass Nowhere Differentiable Function -- 6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and Applications -- 6.2.1 Local Maxima and Minima</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Functions of real variables.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85052357</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Fonctions de variables réelles.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Calculus.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Functions of real variables</subfield><subfield code="2">fast</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Krantz, Steven G.</subfield><subfield code="t">Guide to Real Variables.</subfield><subfield code="d">Washington : Mathematical Association of America, ©2014</subfield><subfield code="z">9780883853443</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Dolciani mathematical expositions.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42009859</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL3330367</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">450274</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7349787</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn775428962 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:18:30Z |
| institution | BVB |
| isbn | 9780883859162 0883859165 |
| language | English |
| oclc_num | 775428962 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (1 online resource) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Dolciani mathematical expositions. |
| series2 | Dolciani Mathematical Expositions ; |
| spelling | Krantz, Steven G. (Steven George), 1951- https://id.oclc.org/worldcat/entity/E39PBJw8VQ7cxG48KCfPym3RKd http://id.loc.gov/authorities/names/n81051364 A Guide to Real Variables / Steven G. Krantz. Cambridge : Cambridge University Press, 2012. 1 online resource (1 online resource) text txt rdacontent computer c rdamedia online resource cr rdacarrier Dolciani Mathematical Expositions ; v. 38 Title from publishers bibliographic system (viewed on 30 Jan 2012). Contents -- Preface -- 1 Basics -- 1.1 Sets -- 1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations on Functions -- 1.5 Number Systems -- 1.5.1 The Real Numbers -- 1.6 Countable and Uncountable Sets -- 2 Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The Definition and Convergence -- 2.1.2 The Cauchy Criterion -- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle -- 2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special Sequences -- 3 Series -- 3.1 Introduction to Series 3.1.1 The Definition and Convergence3.1.2 Partial Sums -- 3.2 Elementary Convergence Tests -- 3.2.1 The Comparison Test -- 3.2.2 The Cauchy Condensation Test -- 3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence -- 3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts -- 3.3.2 Abelâ€?s Test -- 3.3.3 Absolute and Conditional Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other Representations for e -- 3.4.3 Sums of Powers 3.5 Operations on Series3.5.1 Sums and Scalar Products of Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy Product -- 4 The Topology of the Real Line -- 4.1 Open and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets -- 4.1.3 Characterization of Open and Closed Sets in Terms of Sequences -- 4.1.4 Further Properties of Open and Closed Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior Points and Isolated Points -- 4.2.2 Accumulation Points -- 4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction -- 4.4.2 The Heine-Borel Theorem 4.4.3 The Topological Characterization of Compactness4.5 The Cantor Set -- 4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity -- 4.7 Perfect Sets -- 5 Limits and the Continuity of Functions -- 5.1 Definitions and Basic Properties -- 5.1.1 Limits -- 5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of Limits -- 5.1.4 Properties of Limits -- 5.1.5 Characterization of Limits Using Sequences -- 5.2 Continuous Functions -- 5.2.1 Continuity at a Point -- 5.2.2 The Topological Approach to Continuity -- 5.3 Topological Properties and Continuity 5.3.1 The Image of a Function5.3.2 Uniform Continuity -- 5.3.3 Continuity and Connectedness -- 5.3.4 The Intermediate Value Property -- 5.4 Monotonicity and Classifying Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2 Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6 The Derivative -- 6.1 The Concept of Derivative -- 6.1.1 The Definition -- 6.1.2 Properties of the Derivative -- 6.1.3 The Weierstrass Nowhere Differentiable Function -- 6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and Applications -- 6.2.1 Local Maxima and Minima A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize. Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions of real variables fast Print version: Krantz, Steven G. Guide to Real Variables. Washington : Mathematical Association of America, ©2014 9780883853443 Dolciani mathematical expositions. http://id.loc.gov/authorities/names/n42009859 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274 Volltext |
| spellingShingle | Krantz, Steven G. (Steven George), 1951- A Guide to Real Variables / Dolciani mathematical expositions. Contents -- Preface -- 1 Basics -- 1.1 Sets -- 1.2 Operations on Sets -- 1.3 Functions -- 1.4 Operations on Functions -- 1.5 Number Systems -- 1.5.1 The Real Numbers -- 1.6 Countable and Uncountable Sets -- 2 Sequences -- 2.1 Introduction to Sequences -- 2.1.1 The Definition and Convergence -- 2.1.2 The Cauchy Criterion -- 2.1.3 Monotonicity -- 2.1.4 The Pinching Principle -- 2.1.5 Subsequences -- 2.1.6 The Bolzano-Weierstrass Theorem -- 2.2 Limsup and Liminf -- 2.3 Some Special Sequences -- 3 Series -- 3.1 Introduction to Series 3.1.1 The Definition and Convergence3.1.2 Partial Sums -- 3.2 Elementary Convergence Tests -- 3.2.1 The Comparison Test -- 3.2.2 The Cauchy Condensation Test -- 3.2.3 Geometric Series -- 3.2.4 The Root Test -- 3.2.5 The Ratio Test -- 3.2.6 Root and Ratio Tests for Divergence -- 3.3 Advanced Convergence Tests -- 3.3.1 Summation by Parts -- 3.3.2 Abelâ€?s Test -- 3.3.3 Absolute and Conditional Convergence -- 3.3.4 Rearrangements of Series -- 3.4 Some Particular Series -- 3.4.1 The Series for e -- 3.4.2 Other Representations for e -- 3.4.3 Sums of Powers 3.5 Operations on Series3.5.1 Sums and Scalar Products of Series -- 3.5.2 Products of Series -- 3.5.3 The Cauchy Product -- 4 The Topology of the Real Line -- 4.1 Open and Closed Sets -- 4.1.1 Open Sets -- 4.1.2 Closed Sets -- 4.1.3 Characterization of Open and Closed Sets in Terms of Sequences -- 4.1.4 Further Properties of Open and Closed Sets -- 4.2 Other Distinguished Points -- 4.2.1 Interior Points and Isolated Points -- 4.2.2 Accumulation Points -- 4.3 Bounded Sets -- 4.4 Compact Sets -- 4.4.1 Introduction -- 4.4.2 The Heine-Borel Theorem 4.4.3 The Topological Characterization of Compactness4.5 The Cantor Set -- 4.6 Connected and Disconnected Sets -- 4.6.1 Connectivity -- 4.7 Perfect Sets -- 5 Limits and the Continuity of Functions -- 5.1 Definitions and Basic Properties -- 5.1.1 Limits -- 5.1.2 A Limit that Does Not Exist -- 5.1.3 Uniqueness of Limits -- 5.1.4 Properties of Limits -- 5.1.5 Characterization of Limits Using Sequences -- 5.2 Continuous Functions -- 5.2.1 Continuity at a Point -- 5.2.2 The Topological Approach to Continuity -- 5.3 Topological Properties and Continuity 5.3.1 The Image of a Function5.3.2 Uniform Continuity -- 5.3.3 Continuity and Connectedness -- 5.3.4 The Intermediate Value Property -- 5.4 Monotonicity and Classifying Discontinuities -- 5.4.1 Left and Right Limits -- 5.4.2 Types of Discontinuities -- 5.4.3 Monotonic Functions -- 6 The Derivative -- 6.1 The Concept of Derivative -- 6.1.1 The Definition -- 6.1.2 Properties of the Derivative -- 6.1.3 The Weierstrass Nowhere Differentiable Function -- 6.1.4 The Chain Rule -- 6.2 The Mean Value Theorem and Applications -- 6.2.1 Local Maxima and Minima Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions of real variables fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052357 |
| title | A Guide to Real Variables / |
| title_auth | A Guide to Real Variables / |
| title_exact_search | A Guide to Real Variables / |
| title_full | A Guide to Real Variables / Steven G. Krantz. |
| title_fullStr | A Guide to Real Variables / Steven G. Krantz. |
| title_full_unstemmed | A Guide to Real Variables / Steven G. Krantz. |
| title_short | A Guide to Real Variables / |
| title_sort | guide to real variables |
| topic | Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions of real variables fast |
| topic_facet | Functions of real variables. Fonctions de variables réelles. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Functions of real variables |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=450274 |
| work_keys_str_mv | AT krantzsteveng aguidetorealvariables AT krantzsteveng guidetorealvariables |