Problems and solutions for undergraduate analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1998
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 368 S. graph. Darst. |
| ISBN: | 0387982353 9780387982359 |
Staff View
MARC
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| 100 | 1 | |a Shakarchi, Rami |e Verfasser |0 (DE-588)14028138X |4 aut | |
| 245 | 1 | 0 | |a Problems and solutions for undergraduate analysis |c Rami Shakarchi |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XII, 368 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Analysis - Aufgabensammlung | |
| 650 | 7 | |a analisi matematica - [esercizi] |2 tessin-TR | |
| 650 | 4 | |a Mathematical analysis |x Problems, exercises, etc | |
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Record in the Search Index
| _version_ | 1822603424422690817 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
0
SETS
AND
MAPPINGS
1
0.2
MAPPINGS
.
1
0.3
NATURAL
NUMBERS
AND
INDUCTION
.
3
0.4
DENUMERABLE
SETS
.
6
0.5
EQUIVALENCE
RELATIONS
.
7
I
REAL
NUMBERS
9
1.1
ALGEBRAIC
AXIOMS
.
9
1.2
ORDERING
AXIOMS
.
10
1.3
INTEGERS
AND
RATIONAL
NUMBERS
.
13
1.4
THE
COMPLETENESS
AXIOM
.
15
II
LIMITS
AND
CONTINUOUS
FUNCTIONS
19
II.
1
SEQUENCES
OF
NUMBERS
.
19
II.2
FUNCTIONS
AND
LIMITS
.
22
II.3
LIMITS
WITH
INFINITY
.
24
II.4
CONTINUOUS
FUNCTIONS
.
29
III
DIFFERENTIATION
35
III.L
PROPERTIES
OF
THE
DERIVATIVE
.
35
III.2
MEAN
VALUE
THEOREM
.
38
III.3
INVERSE
FUNCTIONS
.
39
X
CONTENTS
IV
ELEMENTARY
FUNCTIONS
43
IV.
1
EXPONENTIAL
.
43
IV.2
LOGARITHM
.
51
IV.3
SINE
AND
COSINE
.
65
IV.4
COMPLEX
NUMBERS
.
71
V
THE
ELEMENTARY
REAL
INTEGRAL
73
V.2
PROPERTIES
OF
THE
INTEGRAL
.
73
V.3
TAYLOR
'
S
FORMULA
.
80
V.4
ASYMPTOTIC
ESTIMATES
AND
STIRLING
'
S
FORMULA
.
84
VI
NORMED
VECTOR
SPACES
91
VI.
2
NORMED
VECTOR
SPACES
.
91
VI.3
N-SPACE
AND
FUNCTION
SPACES
.
96
VI.4
COMPLETENESS
.
99
VI.
5
OPEN
AND
CLOSED
SETS
.
104
VII
LIMITS
111
VII.L
BASIC
PROPERTIES
.
ILL
VII.2
CONTINUOUS
MAPS
.
113
VII.3
LIMITS
IN
FUNCTION
SPACES
.
120
VIII
COMPACTNESS
125
VIII.
1
BASIC
PROPERTIES
OF
COMPACT
SETS
.
125
VIII.2
CONTINUOUS
MAPS
ON
COMPACT
SETS
.
126
VIII.4
RELATION
WITH
OPEN
COVERINGS
.
129
IX
SERIES
133
IX.2
SERIES
OF
POSITIVE
NUMBERS
.
133
IX.3
NON-ABSOHITE
CONVERGENCE
.
146
IX.5
ABSOLUTE
AND
UNIFORM
CONVERGENCE
.
150
IX.6
POWER
SERIES
.
156
IX.
7
DIFFERENTIATION
AND
INTEGRATION
OF
SERIES
.
160
X
THE
INTEGRAL
IN
ONE
VARIABLE
165
X.3
APPROXIMATION
BY
STEP
MAPS
.
165
X.4
PROPERTIES
OF
THE
INTEGRAL
.
170
X.6
RELATION
BETWEEN
THE
INTEGRAL
AND
THE
DERIVATIVE
.
179
XI
APPROXIMATION
WITH
CONVOLUTIONS
183
XI.L
DIRAC
SEQUENCES
.
183
XI.2
THE
WEIERSTRASS
THEOREM
.
185
XII
FOURIER
SERIES
189
XII.
1
HERMITIAN
PRODUCTS
AND
ORTHOGONALITY
.
189
XII.2
TRIGONOMETRIC
POLYNOMIALS
AS
A
TOTAL
FAMILY
.
199
CONTENTS
XI
XII.3
EXPLICIT
UNIFORM
APPROXIMATION
.
203
XII.4
POINTWISE
CONVERGENCE
.
208
XIII
IMPROPER
INTEGRALS
217
XIII.L
DEFINITION
.
217
XIII.2
CRITERIA
FOR
CONVERGENCE
.
219
XIII.3
INTERCHANGING
DERIVATIVES
AND
INTEGRALS
.
225
XIV
THE
FOURIER
INTEGRAL
243
XIV.
1
THE
SCHWARTZ
SPACE
.
243
XIV.2
THE
FOURIER
INVERSION
FORMULA
.
247
XIV.3
AN
EXAMPLE
OF
FOURIER
TRANSFORM
NOT
IN
THE
SCHWARTZ
SPACE
.
250
XV
FUNCTIONS
ON
N-SPACE
253
XV.
1
PARTIAL
DERIVATIVES
.
253
XV.2
DIFFERENTIABILITY
AND
THE
CHAIN
RULE
.
262
XV.3
POTENTIAL
FUNCTIONS
.
266
XV.4
CURVE
INTEGRALS
.
267
XV.5
TAYLOR
'
S
FORMULA
.
273
XV.6
MAXIMA
AND
THE
DERIVATIVE
.
277
XVI
THE
WINDING
NUMBER
AND
GLOBAL
POTENTIAL
FUNCTIONS
287
XVI.2
THE
WINDING
NUMBER
AND
HOMOLOGY
.
287
XVI.5
THE
HOMOTOPY
FORM
OF
THE
INTEGRABILITY
THEOREM
.
288
XVI.6
MORE
ON
HOMOTOPIES
.
290
XVII
DERIVATIVES
IN
VECTOR
SPACES
293
XVII.
1
THE
SPACE
OF
CONTINUOUS
LINEAR
MAPS
.
293
XVII.2
THE
DERIVATIVE
AS
A
LINEAR
MAP
.
295
XVH.3
PROPERTIES
OF
THE
DERIVATIVE
.
296
XVH.4
MEAN
VALUE
THEOREM
.
297
XVH.5
THE
SECOND
DERIVATIVE
.
298
XVH.6
HIGHER
DERIVATIVES
AND
TAYLOR
'
S
FORMULA
.
301
XVIII
INVERSE
MAPPING
THEOREM
303
XVIII.
1
THE
SHRINKING
LEMMA
.
303
XVIII.2
INVERSE
MAPPINGS,
LINEAR
CASE
.
310
XVIII.3
THE
INVERSE
MAPPING
THEOREM
.
318
XVIII.5
PRODUCT
DECOMPOSITIONS
.
320
XIX
ORDINARY
DIFFERENTIAL
EQUATIONS
327
XIX.
1
LOCAL
EXISTENCE
AND
UNIQUENESS
.
327
XIX.3
LINEAR
DIFFERENTIAL
EQUATIONS
.
331
XII
CONTENTS
XX
MULTIPLE
INTEGRALS
337
XX.
1
ELEMENTARY
MULTIPLE
INTEGRATION
.
337
XX.2
CRITERIA
FOR
ADMISSIBILITY
.
343
XX.3
REPEATED
INTEGRALS
.
345
XX.4
CHANGE
OF
VARIABLES
.
346
XX.5
VECTOR
FIELDS
ON
SPHERES
.
358
XXI
DIFFERENTIAL
FORMS
359
XXI.
1
DEFINITIONS
.
359
XXI.3
INVERSE
IMAGE
OF
A
FORM
.
362
XXI.4
STOKES
'
FORMULA
FOR
SIMPLICES
.
363 |
| any_adam_object | 1 |
| author | Shakarchi, Rami |
| author_GND | (DE-588)14028138X |
| author_facet | Shakarchi, Rami |
| author_role | aut |
| author_sort | Shakarchi, Rami |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV011792413 |
| callnumber-first | Q - Science |
| callnumber-label | QA301 |
| callnumber-raw | QA301 |
| callnumber-search | QA301 |
| callnumber-sort | QA 3301 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)245822145 (DE-599)BVBBV011792413 |
| dewey-full | 515.076 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.076 |
| dewey-search | 515.076 |
| dewey-sort | 3515.076 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV011792413 |
| illustrated | Illustrated |
| indexdate | 2025-01-29T17:01:14Z |
| institution | BVB |
| isbn | 0387982353 9780387982359 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007960773 |
| oclc_num | 245822145 |
| open_access_boolean | |
| owner | DE-29 DE-20 DE-83 DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-29 DE-20 DE-83 DE-11 DE-19 DE-BY-UBM |
| physical | XII, 368 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| spelling | Shakarchi, Rami Verfasser (DE-588)14028138X aut Problems and solutions for undergraduate analysis Rami Shakarchi New York [u.a.] Springer 1998 XII, 368 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Analysis - Aufgabensammlung analisi matematica - [esercizi] tessin-TR Mathematical analysis Problems, exercises, etc Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Katze (DE-588)4030046-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Analysis (DE-588)4001865-9 s DE-604 Katze (DE-588)4030046-8 s 1\p DE-604 Infinitesimalrechnung (DE-588)4072798-1 s 2\p DE-604 Algebra (DE-588)4001156-2 s 3\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-1738-1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007960773&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 | Shakarchi, Rami Problems and solutions for undergraduate analysis Analysis - Aufgabensammlung analisi matematica - [esercizi] tessin-TR Mathematical analysis Problems, exercises, etc Infinitesimalrechnung (DE-588)4072798-1 gnd Algebra (DE-588)4001156-2 gnd Katze (DE-588)4030046-8 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4001156-2 (DE-588)4030046-8 (DE-588)4001865-9 (DE-588)4143389-0 |
| title | Problems and solutions for undergraduate analysis |
| title_auth | Problems and solutions for undergraduate analysis |
| title_exact_search | Problems and solutions for undergraduate analysis |
| title_full | Problems and solutions for undergraduate analysis Rami Shakarchi |
| title_fullStr | Problems and solutions for undergraduate analysis Rami Shakarchi |
| title_full_unstemmed | Problems and solutions for undergraduate analysis Rami Shakarchi |
| title_short | Problems and solutions for undergraduate analysis |
| title_sort | problems and solutions for undergraduate analysis |
| topic | Analysis - Aufgabensammlung analisi matematica - [esercizi] tessin-TR Mathematical analysis Problems, exercises, etc Infinitesimalrechnung (DE-588)4072798-1 gnd Algebra (DE-588)4001156-2 gnd Katze (DE-588)4030046-8 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analysis - Aufgabensammlung analisi matematica - [esercizi] Mathematical analysis Problems, exercises, etc Infinitesimalrechnung Algebra Katze Analysis Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007960773&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shakarchirami problemsandsolutionsforundergraduateanalysis |