Elementary analysis: the theory of calculus
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2013
|
| Edition: | 2., [revised] ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 409 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781461462705 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elementary analysis |b the theory of calculus |c Kenneth A. Ross |
| 250 | |a 2., [revised] ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2013 | |
| 300 | |a XI, 409 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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Record in the Search Index
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| adam_text |
Contents
Preface
v
1
Introduction
1
1
The Set
N
of Natural Numbers
. 1
2
The Set
Q
of Rational Numbers
. 6
3
The Set
R
of Real Numbers
. 13
4
The Completeness Axiom
. 20
5
The Symbols
+00
and
—00. 28
6 *
A Development of
R
. 30
2
Sequences
33
7
Limits of Sequences
. 33
8
A Discussion about Proofs
. 39
9
Limit Theorems for Sequences
. 45
10
Monotone Sequences and Cauchy Sequences
. 56
11
Subsequences
. 66
12
lim
sup's and
lim inf
's
. 78
13 *
Some Topological Concepts in Metric Spaces
. 83
14
Series
. 95
15
Alternating Series and Integral Tests
. 105
16 *
Decimal Expansions of Real Numbers
. 109
3
Continuity
123
17
Continuous Functions
. 123
18
Properties of Continuous Functions
. 133
19
Uniform Continuity
. 139
20
Limits of Functions
. 153
21 *
More on Metric Spaces: Continuity
. 164
22 *
More on Metric Spaces: Connectedness
. 178
4
Sequences and Series of Functions
187
23
Power Series
. 187
24
Uniform Convergence
. 193
25
More on Uniform Convergence
. 200
26
Differentiation and Integration of Power Series
. . . 208
27 *
Weierstrass's Approximation Theorem
. 216
5
Differentiation
223
28
Basic Properties of the Derivative
. 223
29
The Mean Value Theorem
. 232
30 *
L'Hospital's Rule
. 241
31
Taylor's Theorem
. 249
6
Integration
269
32
The Riemann Integral
. 269
33
Properties of the Riemann Integral
. 280
34
Fundamental Theorem of Calculus
. 291
35 *
Riemann-Stieltjes Integrals
. 298
36 *
Improper Integrals
. 331
7
Capstone
339
37 *
A Discussion of Exponents and Logarithms
. 339
38 *
Continuous Nowhere-Differentiable Functions
. . . 347
Appendix on Set Notation
365
Selected Hints and Answers
367
A Guide to the References
394
References
„_
Symbols Index
._
Index 405 |
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| bvnumber | BV040736228 |
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| ctrlnum | (OCoLC)852214188 (DE-599)BVBBV040736228 |
| discipline | Mathematik |
| edition | 2., [revised] ed. |
| format | Book |
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| isbn | 9781461462705 |
| language | English |
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| physical | XI, 409 S. graph. Darst. 235 mm x 155 mm |
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| spelling | Ross, Kenneth A. 1936- (DE-588)107448998 aut Elementary analysis the theory of calculus Kenneth A. Ross 2., [revised] ed. New York, NY [u.a.] Springer 2013 XI, 409 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Infinitesimalrechnung (DE-588)4072798-1 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4614-6271-2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025716254&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 | Ross, Kenneth A. 1936- Elementary analysis the theory of calculus Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4001865-9 (DE-588)4151278-9 |
| title | Elementary analysis the theory of calculus |
| title_auth | Elementary analysis the theory of calculus |
| title_exact_search | Elementary analysis the theory of calculus |
| title_full | Elementary analysis the theory of calculus Kenneth A. Ross |
| title_fullStr | Elementary analysis the theory of calculus Kenneth A. Ross |
| title_full_unstemmed | Elementary analysis the theory of calculus Kenneth A. Ross |
| title_short | Elementary analysis |
| title_sort | elementary analysis the theory of calculus |
| title_sub | the theory of calculus |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Infinitesimalrechnung Analysis Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025716254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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