Undergraduate analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon
Springer
1997
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Rev. version of: Analysis 1. |
| Beschreibung: | XV, 642 S. graph. Darst. |
| ISBN: | 0387948414 |
Internformat
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| 100 | 1 | |a Lang, Serge |d 1927-2005 |e Verfasser |0 (DE-588)119305119 |4 aut | |
| 245 | 1 | 0 | |a Undergraduate analysis |c Serge Lang |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1997 | |
| 300 | |a XV, 642 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1807501667449438208 |
|---|---|
| adam_text |
CONTENTS
FOREWORD
TO
THE
FIRST
EDITION
.
V
FOREWORD
TO
THE
SECOND
EDITION
.
IX
PART
ONE
REVIEW
OF
CALCULUS
.
1
CHAPTER
0
SETS
AND
MAPPINGS
.
3
1.
SETS
.
3
2.
MAPPINGS
.
4
3.
NATURAL
NUMBERS
AND
INDUCTION
.
8
4.
DENUMERABLE
SETS
.
11
5.
EQUIVALENCE
RELATIONS
.
15
CHAPTER
I
REAL
NUMBERS
.
17
1.
ALGEBRAIC
AXIOMS
.
17
2.
ORDERING
AXIOMS
.
21
3.
INTEGERS
AND
RATIONAL
NUMBERS
.
25
4.
THE
COMPLETENESS
AXIOM
.
29
CHAPTER
II
LIMITS
AND
CONTINUOUS
FUNCTIONS
.
34
1.
SEQUENCES
OF
NUMBERS
.
34
2.
FUNCTIONS
AND
LIMITS
.
41
XII
CONTENTS
3.
LIMITS
WITH
INFINITY
.
50
4.
CONTINUOUS
FUNCTIONS
.
59
CHAPTER
III
DIFFERENTIATION
.
66
1.
PROPERTIES
OF
THE
DERIVATIVE
.
66
2.
MEAN
VALUE
THEOREM
.
70
3.
INVERSE
FUNCTIONS
.
74
CHAPTER
IV
ELEMENTARY
FUNCTIONS
.
78
1.
EXPONENTIAL
.
78
2.
LOGARITHM
.
83
3.
SINE
AND
COSINE
.
90
4.
COMPLEX
NUMBERS
.
95
CHAPTER
V
THE
ELEMENTARY
REAL
INTEGRAL
.
101
1.
CHARACTERIZATION
OF
THE
INTEGRAL
.
101
2.
PROPERTIES
OF
THE
INTEGRAL
.
104
3.
TAYLOR
'
S
FORMULA
.
109
4.
ASYMPTOTIC
ESTIMATES
AND
STIRLING
'
S
FORMULA
.
116
PART
TWO
CONVERGENCE
.
127
CHAPTER
VI
NORMED
VECTOR
SPACES
.
129
1.
VECTOR
SPACES
.
129
2.
NORMED
VECTOR
SPACES
.
131
3.
N-SPACE
AND
FUNCTION
SPACES
.
137
4.
COMPLETENESS
.
143
5.
OPEN
AND
CLOSED
SETS
.
151
CHAPTER
VII
LIMITS
.
160
1.
BASIC
PROPERTIES
.
160
2.
CONTINUOUS
MAPS
.
170
3.
LIMITS
IN
FUNCTION
SPACES
.
179
4.
COMPLETION
OF
A
NORMED
VECTOR
SPACE
.
188
CONTENTS
XIII
CHAPTER
VIII
COMPACTNESS
.
193
1.
BASIC
PROPERTIES
OF
COMPACT
SETS
.
193
2.
CONTINUOUS
MAPS
ON
COMPACT
SETS
.
197
3.
ALGEBRAIC
CLOSURE
OF
THE
COMPLEX
NUMBERS
.
201
4.
RELATION
WITH
OPEN
COVERINGS
.
203
CHAPTER
IX
SERIES
.
206
1.
BASIC
DEFINITIONS
.
206
2.
SERIES
OF
POSITIVE
NUMBERS
.
208
3.
NON-ABSOLUTE
CONVERGENCE
.
217
4.
ABSOLUTE
CONVERGENCE
IN
VECTOR
SPACES
.
225
5.
ABSOLUTE
AND
UNIFORM
CONVERGENCE
.
229
6.
POWER
SERIES
.
234
7.
DIFFERENTIATION
AND
INTEGRATION
OF
SERIES
.
239
CHAPTER
X
THE
INTEGRAL
IN
ONE
VARIABLE
.
246
1.
EXTENSION
THEOREM
FOR
LINEAR
MAPS
.
246
2.
INTEGRAL
OF
STEP
MAPS
.
248
3.
APPROXIMATION
BY
STEP
MAPS
.
252
4.
PROPERTIES
OF
THE
INTEGRAL
.
255
APPENDIX.
THE
LEBESGUE
INTEGRAL
.
262
5.
THE
DERIVATIVE
.
267
6.
RELATION
BETWEEN
THE
INTEGRAL
AND
THE
DERIVATIVE
.
272
7.
INTERCHANGING
DERIVATIVES
AND
INTEGRALS
.
275
PART
THREE
APPLICATIONS
OF
THE
INTEGRAL
.
281
CHAPTER
XI
APPROXIMATION
WITH
CONVOLUTIONS
.
283
1.
DIRAC
SEQUENCES
.
283
2.
THE
WEIERSTRASS
THEOREM
.
287
CHAPTER
XII
FOURIER
SERIES
.
291
1.
HERMITIAN
PRODUCTS
AND
ORTHOGONALITY
.
291
2.
TRIGONOMETRIC
POLYNOMIALS
AS
A
TOTAL
FAMILY
.
306
3.
EXPLICIT
UNIFORM
APPROXIMATION
.
311
4.
POINTWISE
CONVERGENCE
.
317
XIV
CONTENTS
CHAPTER
XIII
IMPROPER
INTEGRALS
.
326
1.
DEFINITION
.
326
2.
CRITERIA
FOR
CONVERGENCE
.
330
3.
INTERCHANGING
DERIVATIVES
AND
INTEGRALS
.
336
4.
THE
HEAT
KERNEL
.
347
CHAPTER
XIV
THE
FOURIER
INTEGRAL
.
353
1.
THE
SCHWARTZ
SPACE
.
353
2.
THE
FOURIER
INVERSION
FORMULA
.
359
3.
AN
EXAMPLE
OF
FOURIER
TRANSFORM
NOT
IN
THE
SCHWARTZ
SPACE
.
363
PART
FOUR
CALCULUS
IN
VECTOR
SPACES
.
369
CHAPTER
XV
FUNCTIONS
ON
N-SPACE
.
371
1.
PARTIAL
DERIVATIVES
.
371
2.
DIFFERENTIABILITY
AND
THE
CHAIN
RULE
.
379
3.
POTENTIAL
FUNCTIONS
.
388
4.
CURVE
INTEGRALS
.
395
5.
TAYLOR
'
S
FORMULA
.
405
6.
MAXIMA
AND
THE
DERIVATIVE
.
411
CHAPTER
XVI
THE
WINDING
NUMBER
AND
GLOBAL
POTENTIAL
FUNCTIONS
.
417
1.
ANOTHER
DESCRIPTION
OF
THE
INTEGRAL
ALONG
A
PATH
.
418
2.
THE
WINDING
NUMBER
AND
HOMOLOGY
.
420
3.
PROOF
OF
THE
GLOBAL
INTEGRABILITY
THEOREM
.
432
4.
THE
INTEGRAL
OVER
CONTINUOUS
PATHS
.
438
5.
THE
HOMOTOPY
FORM
OF
THE
INTEGRABILITY
THEOREM
.
444
6.
MORE
ON
HOMOTOPIES
.
450
CHAPTER
XVII
DERIVATIVES
IN
VECTOR
SPACES
.
455
1.
THE
SPACE
OF
CONTINUOUS
LINEAR
MAPS
.
455
2.
THE
DERIVATIVE
AS
A
LINEAR
MAP
.
463
3.
PROPERTIES
OF
THE
DERIVATIVE
.
468
4.
MEAN
VALUE
THEOREM
.
473
CONTENTS
XV
5.
THE
SECOND
DERIVATIVE
.
.
477
6.
HIGHER
DERIVATIVES
AND
TAYLOR
'
S
FORMULA
.
487
7.
PARTIAL
DERIVATIVES
.
495
8.
DIFFERENTIATING
UNDER
THE
INTEGRAL
SIGN
.
499
CHAPTER
XVIII
INVERSE
MAPPING
THEOREM
.
502
1.
THE
SHRINKING
LEMMA
.
502
2.
INVERSE
MAPPINGS,
LINEAR
CASE
.
506
3.
THE
INVERSE
MAPPING
THEOREM
.
512
4.
IMPLICIT
FUNCTIONS
AND
CHARTS
.
520
5.
PRODUCT
DECOMPOSITIONS
.
526
CHAPTER
XIX
ORDINARY
DIFFERENTIAL
EQUATIONS
.
538
1.
LOCAL
EXISTENCE
AND
UNIQUENESS
.
538
2.
APPROXIMATE
SOLUTIONS
.
548
3.
LINEAR
DIFFERENTIAL
EQUATIONS
.
552
4.
DEPENDENCE
ON
INITIAL
CONDITIONS
.
557
PART
FIVE
MULTIPLE
INTEGRATION
.
563
CHAPTER
XX
MULTIPLE
INTEGRALS
.
565
1.
ELEMENTARY
MULTIPLE
INTEGRATION
.
565
2.
CRITERIA
FOR
ADMISSIBILITY
.
578
3.
REPEATED
INTEGRALS
.
581
4.
CHANGE
OF
VARIABLES
.
584
5.
VECTOR
FIELDS
ON
SPHERES
.
602
CHAPTER
XXI
DIFFERENTIAL
FORMS
.
607
1.
DEFINITIONS
.
607
2.
STOKES
'
THEOREM
FOR
A
RECTANGLE
.
613
3.
INVERSE
IMAGE
OF
A
FORM
.
616
4.
STOKES
'
FORMULA
FOR
SIMPLICES
.
620
APPENDIX
.
627
INDEX
.
635 |
| any_adam_object | 1 |
| author | Lang, Serge 1927-2005 |
| author_GND | (DE-588)119305119 |
| author_facet | Lang, Serge 1927-2005 |
| author_role | aut |
| author_sort | Lang, Serge 1927-2005 |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV011230871 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300.L278 1997 |
| callnumber-search | QA300.L278 1997 |
| callnumber-sort | QA 3300 L278 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)263858173 (DE-599)BVBBV011230871 |
| dewey-full | 515/.820 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 20 |
| dewey-search | 515/.8 20 |
| dewey-sort | 3515 18 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV011230871 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:25:15Z |
| institution | BVB |
| isbn | 0387948414 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007536415 |
| oclc_num | 263858173 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-521 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-521 DE-11 |
| physical | XV, 642 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Undergraduate analysis Serge Lang 2. ed. New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon Springer 1997 XV, 642 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Rev. version of: Analysis 1. Mathematical analysis 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)4123623-3 Lehrbuch 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 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007536415&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 | Lang, Serge 1927-2005 Undergraduate analysis Mathematical analysis 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)4123623-3 |
| title | Undergraduate analysis |
| title_auth | Undergraduate analysis |
| title_exact_search | Undergraduate analysis |
| title_full | Undergraduate analysis Serge Lang |
| title_fullStr | Undergraduate analysis Serge Lang |
| title_full_unstemmed | Undergraduate analysis Serge Lang |
| title_short | Undergraduate analysis |
| title_sort | undergraduate analysis |
| topic | Mathematical analysis 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 | Mathematical analysis Infinitesimalrechnung Algebra Katze Analysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007536415&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT langserge undergraduateanalysis |