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: | |
| Links: | 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 |
| Physical Description: | XI, 409 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781461462705 |
Staff View
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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 | |
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Record in the Search Index
| _version_ | 1819276632861442048 |
|---|---|
| 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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| discipline | Mathematik |
| edition | 2., [revised] ed. |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV040736228 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:24:36Z |
| institution | BVB |
| isbn | 9781461462705 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025716254 |
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| physical | XI, 409 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| 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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