Introduction to calculus and classical analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
2007
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 337 S. graph. Darst. |
| ISBN: | 9780387693156 0387693157 9781441924094 |
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Datensatz im Suchindex
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|---|---|
| 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. |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| edition | 2. ed. |
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| 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 |
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| title | Introduction to calculus and classical analysis |
| title_auth | Introduction to calculus and classical analysis |
| title_exact_search | Introduction to calculus and classical analysis |
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| title_full | Introduction to calculus and classical analysis Omar Hijab |
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| title_short | Introduction to calculus and classical analysis |
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