A preliminary course in analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Chapman and Hall
1968
|
| Series: | Chapman and Hall mathematics series.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII,213 S.m.Abb. |
Staff View
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Record in the Search Index
| _version_ | 1804119896618958848 |
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| adam_text | Contents
Authors Preface page vii
1. Sets, relations and functions
1.1. Sets 1
1.2. Venn diagrams and the combination of sets 6
1.3. Relations 10
1.4. Functions 13
1.5. Standard notations for functions 17
1.6. Direct and inverse images 21
1.7. Transitive and order relations 27
1.8. Basic facts about the sets Q and R 29
1.9. Complex numbers 35
2. Continuity and differentiability
2.1. Continuity of real functions 41
2.2. Rules for combining continuous functions 51
2.3. Continuity of complex functions 62
2.4. Differentiability 65
2.5. Rules on differentiability 70
2.6. Maxima and minima 77
3. The completeness of R and its consequences
3.1. The real numbers 81
3.2. The intermediate value theorem 87
3.3. Boundedness of real functions 91
3.4. Functions differentiable on intervals 96
3.5. Inverse functions 102
xi
xii CONTENTS
4. Integration and its applications
4.1. Antidifferentiation page 113
4.2. The definite integral 116
4.3. The relation between antiderivatives and definite integrals 123
4.4. Rules for integration 127
4.5. Logarithmic and exponential functions 135
4.6. The trigonometric functions 144
4.7. The complex exponential and logarithmic functions 153
4.8. Taylor s theorem 163
5. Sequences and series
5.1. Sequences 171
5.2. Rules for limits 178
5.3. Bounded monotonic sequences 185
5.4. Series 189
5.5. Tests for convergence of series 195
Glossary of symbols 207
Index 211
|
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| indexdate | 2024-07-09T16:33:29Z |
| institution | BVB |
| language | English |
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| publishDate | 1968 |
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| series2 | Chapman and Hall mathematics series. |
| spelling | Moss, Robert M. F. Verfasser aut A preliminary course in analysis Robert Michael Forrester Moss ; Geoffrey T. Roberts* London Chapman and Hall 1968 XII,213 S.m.Abb. txt rdacontent n rdamedia nc rdacarrier Chapman and Hall mathematics series. Analyse (wiskunde) gtt Analyse mathématique Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Roberts, Geoffrey T. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moss, Robert M. F. Roberts, Geoffrey T. A preliminary course in analysis Analyse (wiskunde) gtt Analyse mathématique Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4151278-9 |
| title | A preliminary course in analysis |
| title_auth | A preliminary course in analysis |
| title_exact_search | A preliminary course in analysis |
| title_full | A preliminary course in analysis Robert Michael Forrester Moss ; Geoffrey T. Roberts* |
| title_fullStr | A preliminary course in analysis Robert Michael Forrester Moss ; Geoffrey T. Roberts* |
| title_full_unstemmed | A preliminary course in analysis Robert Michael Forrester Moss ; Geoffrey T. Roberts* |
| title_short | A preliminary course in analysis |
| title_sort | a preliminary course in analysis |
| topic | Analyse (wiskunde) gtt Analyse mathématique Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse (wiskunde) Analyse mathématique Mathematical analysis Analysis Einführung |
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