Elementary analysis: the theory of Calculus
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K
Springer
1993
|
| Edition: | 6., corr. pr. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 264 S. graph. Darst. |
| ISBN: | 354090459X 038790459X |
Staff View
MARC
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| 245 | 1 | 0 | |a Elementary analysis |b the theory of Calculus |c Kenneth A. Ross |
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| 300 | |a VIII, 264 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1807321308566913024 |
|---|---|
| adam_text |
CONTENTS
CHAPTER
I
INTRODUCTION
1
§
1
THE
SET
N
OF
NATURAL
NUMBERS
1
§2
THE
SET
Q
OF
RATIONAL
NUMBERS
5
§3
THE
SET
R
OF
REAL
NUMBERS
10
§4
THE
COMPLETENESS
AXIOM
14
§5
THE
SYMBOLS
+
AND
-
00
20
§6*
A
DEVELOPMENT
OF
R
22
CHAPTER
II
SEQUENCES
24
§7
LIMITS
OF
SEQUENCES
24
§8
A
DISCUSSION
ABOUT
PROOFS
28
§9
LIMIT
THEOREMS
FOR
SEQUENCES
33
§10
MONOTONE
SEQUENCES
AND
CAUCHY
SEQUENCES
42
§
11
SUBSEQUENCES
48
§12
LIM
SUP
'
S
AND
LIM
INF
'
S
57
§13*
SOME
TOPOLOGICAL
CONCEPTS
IN
METRIC
SPACES
60
§
14
SERIES
$$
§15
ALTERNATING
SERIES
AND
INTEGRAL
TESTS
76
§16*
DECIMAL
EXPANSIONS
OF
REAL
NUMBERS
79
YYOPTIONAL
SECTIONS.
VII
VIII
CONTENTS
CHAPTER
III
CONTINUITY
87
§17
CONTINUOUS
FUNCTIONS
87
§18
PROPERTIES
OF
CONTINUOUS
FUNCTIONS
95
§19
UNIFORM
CONTINUITY
100
§20
LIMITS
OF
FUNCTIONS
110
§21*
MORE
ON
METRIC
SPACES:
CONTINUITY
118
§22*
MORE
ON
METRIC
SPACES:
CONNECTEDNESS
124
CHAPTER
IV
SEQUENCES
AND
SERIES
OF
FUNCTIONS
129
§23
POWER
SERIES
129
§24
UNIFORM
CONVERGENCE
133
§25
MORE
ON
UNIFORM
CONVERGENCE
139
§26
DIFFERENTIATION
AND
INTEGRATION
OF
POWER
SERIES
145
§27*
WEIERSTRASS
'
S
APPROXIMATION
THEOREM
150
CHAPTER
V
DIFFERENTIATION
155
§28
BASIC
PROPERTIES
OF
THE
DERIVATIVE
155
§29
THE
MEAN
VALUE
THEOREM
161
§30*
L
'
HOSPITAL
'
S
RULE
168
§31
TAYLOR
'
S
THEOREM
175
CHAPTER
VI
INTEGRATION
184
§32
THE
RIEMANN
INTEGRAL
184
§33
PROPERTIES
OF
THE
RIEMANN
INTEGRAL
192
§34
FUNDAMENTAL
THEOREM
OF
CALCULUS
198
§35*
RIEMANN
-
STIELTJES
INTEGRALS
203
§36*
IMPROPER
INTEGRALS
221
§37*
A
DISCUSSION
ON
EXPONENTS
AND
LOGARITHMS
226
APPENDIX
ON
SET
NOTATION
233
SELECTED
HINTS
AND
ANSWERS
235
BIBLIOGRAPHY
258
SYMBOLS
INDEX
260
SUBJECT
INDEX
261 |
| any_adam_object | 1 |
| author | Ross, Kenneth A. 1936- |
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| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)29848306 (DE-599)BVBBV009129567 |
| 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 | 6., corr. pr. |
| format | Book |
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| physical | VIII, 264 S. graph. Darst. |
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| spelling | Ross, Kenneth A. 1936- Verfasser (DE-588)107448998 aut Elementary analysis the theory of Calculus Kenneth A. Ross 6., corr. pr. New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K Springer 1993 VIII, 264 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Calcul infinitésimal ram Calculus Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Analysis (DE-588)4001865-9 s 3\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006051538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ross, Kenneth A. 1936- Elementary analysis the theory of Calculus Calcul infinitésimal ram 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 (DE-588)4123623-3 |
| 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 | Calcul infinitésimal ram Calculus Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Calcul infinitésimal Calculus Infinitesimalrechnung Analysis Einführung Lehrbuch |
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