Principles of mathematical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
McGraw-Hill
[ca. 2010]
|
| Edition: | 3. ed., [Nachdr.] |
| Series: | International series in pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 342 S. |
| ISBN: | 9780070542358 007054235X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804145594210451456 |
|---|---|
| adam_text | CONTENTS
Preface
ix
Chapter
1
The Real and Complex Number Systems
1
Introduction
1
Ordered Sets
3
Fields
5
The Real Field
8
The Extended Real Number System
11
The Complex Field
12
Euclidean Spaces
16
Appendix
17
Exercises
21
Chapter
2
Basic Topology
24
Finite, Countable, and Uncountable Sets
24
Metric Spaces
30
Compact Sets
36
Perfect Sets
41
VÍ
CONTENTS
Connected Sets
42
Exercises
43
Chapter
3
Numerical Sequences and Series
47
Convergent Sequences
47
Subsequences
51
Cauchy Sequences
52
Upper and Lower Limits
55
Some Special Sequences
57
Series
58
Series of
Nonnegative
Terms
61
The Number
e
63
The Root and Ratio Tests
65
Power Series
69
Summation by Parts
70
Absolute Convergence
71
Addition and Multiplication of Series
72
Rearrangements
75
Exercises
78
Chapter
4
Continuity
83
Limits of Functions
83
Continuous Functions
85
Continuity and Compactness
89
Continuity and Connectedness
93
Discontinuities
94
Monotonie
Functions
95
Infinite Limits and Limits at Infinity
97
Exercises
98
Chapter
5
Differentiation
103
The Derivative of a Real Function
103
Mean Value Theorems
107
The Continuity of Derivatives
108
L Hospital s Rule
109
Derivatives of Higher Order
110
Taylor s Theorem
110
Differentiation of Vector-valued Functions 111
Exercises
114
CONTENTS
VU
Chapter
6
The Riemann-Stieltjes Integral
120
Definition and Existence of the Integral
120
Properties of the Integral
128
Integration and Differentiation
133
Integration of Vector-valued Functions
135
Rectifiable Curves
136
Exercises
138
Chapter
7
Sequences and Series of Functions,
143
Discussion of Main Problem
143
Uniform Convergence
147
Uniform Convergence and Continuity
149
Uniform Convergence and Integration
151
Uniform Convergence and Differentiation
152
Equicontinuous Families of Functions
154
The
Sto ne-Weierstrass
Theorem
159
Exercises
165
Chapter
8
Some Special Functions
172
Power Series
172
The Exponential and Logarithmic Functions
178
The Trigonometric Functions
182
The Algebraic Completeness of the Complex Field
184
Fourier Series
185
The Gamma Function
192
Exercises
196
Chapter
9
Functions of Several Variables
204
Linear Transformations
204
Differentiation
211
The Contraction Principle
220
The Inverse Function Theorem
221
The Implicit Function Theorem
223
The Rank Theorem
228
Determinants
231
Derivatives of Higher Order
235
Differentiation of Integrals
236
Exercises
239
Chapter
10
Integration of Differential Forms
245
Integration
245
titt
CONTENTS
Primitive Mappings
248
Partitions of Unity
251
Change of Variables
252
Differential Forms
253
Simplexes
and Chains
266
Stokes Theorem
273
Closed Forms and Exact Forms
275
Vector Analysis
280
Exercises
288
Chapter
11
The Lebesgue Theory
300
Set Functions
300
Construction of the Lebesgue Measure
302
Measure Spaces
310
Measurable Functions
310
Simple Functions
313
Integration
314
Comparison with the Riemann Integral
322
Integration of Complex Functions
325
Functions of Class
£Єг
325
Exercises
332
Bibliography
335
List of Special Symbols
337
Index
339
|
| any_adam_object | 1 |
| author | Rudin, Walter 1921-2010 |
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| callnumber-label | QA300 |
| callnumber-raw | QA300.R8 1976 |
| callnumber-search | QA300.R8 1976 |
| callnumber-sort | QA 3300 R8 41976 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)729950323 (DE-599)BVBBV037316808 |
| 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 |
| edition | 3. ed., [Nachdr.] |
| format | Book |
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| isbn | 9780070542358 007054235X |
| language | English |
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| physical | X, 342 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | McGraw-Hill |
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| series2 | International series in pure and applied mathematics |
| spelling | Rudin, Walter 1921-2010 Verfasser (DE-588)119445670 aut Principles of mathematical analysis Walter Rudin 3. ed., [Nachdr.] New York, NY [u.a.] McGraw-Hill [ca. 2010] X, 342 S. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Mathematical analysis Grundlage (DE-588)4158388-7 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Analysis (DE-588)4001865-9 s DE-604 Grundlage (DE-588)4158388-7 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022471102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rudin, Walter 1921-2010 Principles of mathematical analysis Mathematical analysis Grundlage (DE-588)4158388-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4158388-7 (DE-588)4001865-9 (DE-588)4123623-3 |
| title | Principles of mathematical analysis |
| title_auth | Principles of mathematical analysis |
| title_exact_search | Principles of mathematical analysis |
| title_full | Principles of mathematical analysis Walter Rudin |
| title_fullStr | Principles of mathematical analysis Walter Rudin |
| title_full_unstemmed | Principles of mathematical analysis Walter Rudin |
| title_short | Principles of mathematical analysis |
| title_sort | principles of mathematical analysis |
| topic | Mathematical analysis Grundlage (DE-588)4158388-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Grundlage Analysis Lehrbuch |
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