Introduction to calculus and classical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
2007
|
| Edition: | 2. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 337 S. graph. Darst. |
| ISBN: | 9780387693156 0387693157 9781441924094 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023116136 | ||
| 003 | DE-604 | ||
| 005 | 20130318 | ||
| 007 | t | ||
| 008 | 080206s2007 gw d||| |||| 00||| ger d | ||
| 020 | |a 9780387693156 |9 978-0-387-69315-6 | ||
| 020 | |a 0387693157 |9 0-387-69315-7 | ||
| 020 | |a 9781441924094 |c PoDAusg. |9 978-1-4419-2409-4 | ||
| 035 | |a (OCoLC)255964668 | ||
| 035 | |a (DE-599)BVBBV023116136 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-20 |a DE-11 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA303 | |
| 082 | 0 | |a 515 | |
| 084 | |a SK 399 |0 (DE-625)143236: |2 rvk | ||
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 084 | |a 70H20 |2 msc | ||
| 084 | |a 26-01 |2 msc | ||
| 084 | |a 47-02 |2 msc | ||
| 084 | |a 49-01 |2 msc | ||
| 100 | 1 | |a Hijab, Omar |e Verfasser |0 (DE-588)115519351 |4 aut | |
| 245 | 1 | 0 | |a Introduction to calculus and classical analysis |c Omar Hijab |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2007 | |
| 300 | |a X, 337 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Infinitesimalrechnung |0 (DE-588)4072798-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Infinitesimalrechnung |0 (DE-588)4072798-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016318658 | ||
Record in the Search Index
| _version_ | 1804137381717082112 |
|---|---|
| adam_text | Titel: Introduction to calculus and classical analysis
Autor: Hijab, Omar
Jahr: 2007
Contents
1 The Set of Real Numbers ..................................................................1
1.1 Sets and Mappings............................................................................1
1.2 The Set R............................................................................................3
1.3 The Subset N and the Principle of Induction ..............................7
1.4 The Completeness Property ............................................................13
1.5 Sequences and Limits ......................................................................17
1.6 Nonncgativc Series and Decimal Expansions................................27
1.7 Signed Series and Cauchy Sequences ............................................32
2 Continuity..................................................................................................43
2.1 Compactness........................................................................................43
2.2 Continuous Limits..............................................................................44
2.3 Continuous Functions........................................................................48
3 Differentiation ............................................ 63
3.1 Derivatives............................................. 63
3.2 Mapping Properties...................................... 71
3.3 Graphing Techniques .................................... 77
3.4 Power Series............................................ 87
3.5 Trigonometry .......................................... 99
3.6 Primitives..............................................108
4 Integration ................................................115
4.1 The Cantor Set .........................................115
4.2 Area...................................................119
4.3 The Integral ...........................................134
4.4 The Fundamental Theorem of Calculus ....................151
4.5 The Method of Exhaustion ...............................161
X
Contents
5 Applications...............................................173
5.1 Euler s Gamma Function.................................173
5.2 The Number ............................................179
5.3 Gauss Arithmetic-Geometric Mean (AGM).................192
5.4 The Gaussian Integral....................................201
5.5 Stirling s Approximation of n!.............................210
5.6 Infinite Products........................................21C
5.7 Jacobi s Theta Functions.................................225
5.8 Ricmann s Zeta Function ................................231
5.9 The Euler-Maclaurin Formula ............................241
A Solutions..................................................249
A.l Solutions to Chapter 1...................................249
A.2 Solutions to Chapter 2...................................263
A.3 Solutions to Chapter 3...................................270
A.4 Solutions to Chapter 4...................................289
A.5 Solutions to Chapter 5...................................307
References.....................................................331
Index.............................................................
|
| adam_txt |
Titel: Introduction to calculus and classical analysis
Autor: Hijab, Omar
Jahr: 2007
Contents
1 The Set of Real Numbers .1
1.1 Sets and Mappings.1
1.2 The Set R.3
1.3 The Subset N and the Principle of Induction .7
1.4 The Completeness Property .13
1.5 Sequences and Limits .17
1.6 Nonncgativc Series and Decimal Expansions.27
1.7 Signed Series and Cauchy Sequences .32
2 Continuity.43
2.1 Compactness.43
2.2 Continuous Limits.44
2.3 Continuous Functions.48
3 Differentiation . 63
3.1 Derivatives. 63
3.2 Mapping Properties. 71
3.3 Graphing Techniques . 77
3.4 Power Series. 87
3.5 Trigonometry . 99
3.6 Primitives.108
4 Integration .115
4.1 The Cantor Set .115
4.2 Area.119
4.3 The Integral .134
4.4 The Fundamental Theorem of Calculus .151
4.5 The Method of Exhaustion .161
X
Contents
5 Applications.173
5.1 Euler's Gamma Function.173
5.2 The Number .179
5.3 Gauss' Arithmetic-Geometric Mean (AGM).192
5.4 The Gaussian Integral.201
5.5 Stirling's Approximation of n!.210
5.6 Infinite Products.21C
5.7 Jacobi's Theta Functions.225
5.8 Ricmann's Zeta Function .231
5.9 The Euler-Maclaurin Formula .241
A Solutions.249
A.l Solutions to Chapter 1.249
A.2 Solutions to Chapter 2.263
A.3 Solutions to Chapter 3.270
A.4 Solutions to Chapter 4.289
A.5 Solutions to Chapter 5.307
References.331
Index. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hijab, Omar |
| author_GND | (DE-588)115519351 |
| author_facet | Hijab, Omar |
| author_role | aut |
| author_sort | Hijab, Omar |
| author_variant | o h oh |
| building | Verbundindex |
| bvnumber | BV023116136 |
| callnumber-first | Q - Science |
| callnumber-label | QA303 |
| callnumber-raw | QA303 |
| callnumber-search | QA303 |
| callnumber-sort | QA 3303 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 399 SK 400 |
| ctrlnum | (OCoLC)255964668 (DE-599)BVBBV023116136 |
| 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 |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01845nam a2200529 c 4500</leader><controlfield tag="001">BV023116136</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130318 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080206s2007 gw d||| |||| 00||| ger d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387693156</subfield><subfield code="9">978-0-387-69315-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387693157</subfield><subfield code="9">0-387-69315-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441924094</subfield><subfield code="c">PoDAusg.</subfield><subfield code="9">978-1-4419-2409-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)255964668</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023116136</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA303</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 399</subfield><subfield code="0">(DE-625)143236:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 400</subfield><subfield code="0">(DE-625)143237:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">70H20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">26-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47-02</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">49-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hijab, Omar</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115519351</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to calculus and classical analysis</subfield><subfield code="c">Omar Hijab</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 337 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Undergraduate texts in mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calculus</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Infinitesimalrechnung</subfield><subfield code="0">(DE-588)4072798-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Infinitesimalrechnung</subfield><subfield code="0">(DE-588)4072798-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016318658</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV023116136 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:50:02Z |
| indexdate | 2024-07-09T21:11:24Z |
| institution | BVB |
| isbn | 9780387693156 0387693157 9781441924094 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016318658 |
| oclc_num | 255964668 |
| open_access_boolean | |
| owner | DE-20 DE-11 DE-83 DE-188 |
| owner_facet | DE-20 DE-11 DE-83 DE-188 |
| physical | X, 337 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Hijab, Omar Verfasser (DE-588)115519351 aut Introduction to calculus and classical analysis Omar Hijab 2. ed. New York [u.a.] Springer 2007 X, 337 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Calculus Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Analysis (DE-588)4001865-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hijab, Omar Introduction to calculus and classical analysis Calculus Mathematical analysis Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4072798-1 (DE-588)4123623-3 |
| title | Introduction to calculus and classical analysis |
| title_auth | Introduction to calculus and classical analysis |
| title_exact_search | Introduction to calculus and classical analysis |
| title_exact_search_txtP | Introduction to calculus and classical analysis |
| title_full | Introduction to calculus and classical analysis Omar Hijab |
| title_fullStr | Introduction to calculus and classical analysis Omar Hijab |
| title_full_unstemmed | Introduction to calculus and classical analysis Omar Hijab |
| title_short | Introduction to calculus and classical analysis |
| title_sort | introduction to calculus and classical analysis |
| topic | Calculus Mathematical analysis Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Calculus Mathematical analysis Analysis Infinitesimalrechnung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318658&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hijabomar introductiontocalculusandclassicalanalysis |