Berkeley problems in mathematics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Problem books in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 581 - 587 |
| Beschreibung: | XIV, 591 S. graph. Darst. |
| ISBN: | 0387008926 0387204296 |
Internformat
MARC
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| 100 | 1 | |a De Souza, Paulo Ney |e Verfasser |0 (DE-588)120560542 |4 aut | |
| 245 | 1 | 0 | |a Berkeley problems in mathematics |c Paulo Ney de Souza ; Jorge-Nuno Silva |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XIV, 591 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Problem books in mathematics | |
| 500 | |a Literaturverz. S. 581 - 587 | ||
| 610 | 2 | 4 | |a University of California, Berkeley. |b Dept. of Mathematics |x Examinations |
| 610 | 2 | 7 | |a University of California Berkeley |0 (DE-588)2025100-2 |2 gnd |9 rswk-swf |
| 650 | 7 | |a Matemática (problemas e exercícios) |2 larpcal | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematikstudium |0 (DE-588)4037947-4 |2 gnd |9 rswk-swf |
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| 689 | 2 | 1 | |a Mathematikstudium |0 (DE-588)4037947-4 |D s |
| 689 | 2 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Silva, Jorge-Nuno |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012859868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012859868 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804132849635295232 |
|---|---|
| adam_text | Contents
Preface
vii
I Problems
1
1
Real Analysis
3
1.1
Elementary Calculus
....................... 3
1.2
Limits and Continuity
...................... 8
1.3
Sequences, Series, and Products
................. 10
1.4
Differential Calculus
....................... 14
1.5
Integral Calculus
......................... 18
1.6
Sequences of Functions
..................... 22
1.7
Fourier Series
........................... 27
1.8
Convex Functions
........................ 29
2
Multi
variable Calculus
31
2.1
Limits and Continuity
...................... 31
2.2
Differential Calculus
....................... 32
2.3
Integral Calculus
......................... 40
3
Differential Equations
43
3.1
First Order Equations
....................... 43
3.2
Second Order Equations
..................... 47
xii Contents
3.3 Higher Order
Equations
.....................49
3.4 Systems
of
Differential
Equations
................50
4
Metric
Spaces 57
4.1
Topology of
R ..........................
57
4.2
General
Theory
.......................... 60
4.3
Fixed
Point
Theorem
....................... 62
5
Complex Analysis
65
5.1
Complex Numbers
........................ 65
5.2
Series and Sequences of Functions
................ 67
5.3
Conformai
Mappings
....................... 70
5.4
Functions on the Unit Disc
..................... 71
5.5
Growth Conditions
........................74
5.6
Analytic and Meromorphic Functions
..............75
5.7
Cauchy s Theorem
........................ 80
5.8
Zeros and Singularities
...................... 82
5.9
Harmonic Functions
....................... 86
5.10
Residue Theory
.......................... 87
5.11
Integrals Along the Real Axis
.................. 93
6
Algebra
97
6.1
Examples of Groups and General Theory
............97
6.2
Homomorphisms and Subgroups
.................99
6.3
Cyclic Groups
..........................102
6.4
Normality, Quotients, and Homornorphisms
...........102
6.5
Sn,An,Dn,
.............................104
6.6
Direct Products
..........................106
6.7
Free Groups, Generators, and Relations
.............106
6.8
Finite Groups
...........................107
6.9
Rings and Their Homomorphisms
................109
6.10
Ideals
...............................
Ill
6.11
Polynomials
...........................112
6.12
Fields and Their Extensions
...................116
6.13
Elementary Number Theory
...................118
7
Linear Algebra
123
7.1
Vector Spaces
...........................123
7.2
Rank and Determinants
......................125
7.3
Systems of Equations
.......................129
7.4
Linear Transformations
......................129
7.5
Eigenvalues and Eigenvectors
..................134
7.6
Canonical Forms
.........................138
7.7
Similarity
.............................144
7.8
Bilinear, Quadratic Forms, and Inner Product Spaces
......146
Contents xiii
7.9 General
Theory of
Matrices
...................149
II
Solutions
155
1
Rea!
Analysis
157
1.1
Elementary Calculus
.......................157
1.2
Limits and Continuity
......................173
1.3
Sequences, Series, and Products
.................178
1.4
Differential Calculus
.......................191
1.5
Integral Calculus
.........................200
1.6
Sequences of Functions
.....................213
1.7
Fourier Series
...........................228
1.8
Convex Functions
........................232
2 Multivariable
Calculus
235
2.1
Limits and Continuity
......................235
2.2
Differential Calculus
.......................237
2.3
Integral Calculus
.........................258
3
Differential Equations
265
3.1
First Order Equations
.......................265
3.2
Second Order Equations
.....................274
3.3
Higher Order Equations
.....................278
3.4
Systems of Differential Equations
................280
4
Metric Spaces
289
4.1
Topology of R
..........................289
4.2
General Theory
..........................297
4.3
Fixed Point Theorem
.......................300
5
Complex Analysis
305
5.1
Complex Numbers
........................305
5.2
Series and Sequences of Functions
................ 309
5.3
Conformai
Mappings
.......................316
5.4
Functions on the Unit Disc
....................321
5.5
Growth Conditions
........................329
5.6
Analytic and Meromorphic Functions
..............334
5.7
Cauchy s Theorem
........................347
5.8
Zeros and Singularities
......................356
5.9
Harmonic Functions
.......................372
5.10
Residue Theory
..........................373
5.11
Integrals Along the Real Axis
..................390
6
Algebra
423
6.1
Examples of Groups and General Theory
............423
xiv Contents
6.2 Homomorphismsand
Subgroups
.................429
6.3
Cyclic Groups
..........................433
6.4
Normality, Quotients, and Homomorphisms
........... 435
6.5 S„,A„,Dn,.............................440
6.6
Direct Products
..........................443
6.7
Free Groups, Generators, and Relations
............. 445
6.8
Finite Groups
...........................450
6.9
Rings and Their Homomorphisms
................456
6.10
Ideals
...............................460
6.11
Polynomials
...........................463
6.12
Fields and Their Extensions
...................473
6.13
Elementary Number Theory
...................480
7
Linear Algebra
489
7.1
Vector Spaces
...........................489
7.2
Rank and Determinants
......................495
7.3
Systems of Equations
.......................501
7.4
Linear Transformations
......................503
7.5
Eigenvalues and Eigenvectors
..................514
7.6
Canonical Forms
.........................525
7.7
Similarity
.............................540
7.8
Bilinear, Quadratic Forms, and Inner Product Spaces
......545
7.9
General Theory of Matrices
...................553
III Appendices
569
A How to Get the Exams
571
A.I On-line
..............................571
A.2 Off-line, the Last Resort
.....................571
8
Passing Scores
577
С
The Syllabus
579
References
581
Index
589
|
| any_adam_object | 1 |
| author | De Souza, Paulo Ney Silva, Jorge-Nuno |
| author_GND | (DE-588)120560542 |
| author_facet | De Souza, Paulo Ney Silva, Jorge-Nuno |
| author_role | aut aut |
| author_sort | De Souza, Paulo Ney |
| author_variant | s p n d spn spnd j n s jns |
| building | Verbundindex |
| bvnumber | BV019397455 |
| callnumber-first | Q - Science |
| callnumber-label | QA43 |
| callnumber-raw | QA43 |
| callnumber-search | QA43 |
| callnumber-sort | QA 243 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SM 930 |
| ctrlnum | (OCoLC)53331095 (DE-599)BVBBV019397455 |
| dewey-full | 510/.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.76 |
| dewey-search | 510/.76 |
| dewey-sort | 3510 276 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV019397455 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:22Z |
| institution | BVB |
| isbn | 0387008926 0387204296 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012859868 |
| oclc_num | 53331095 |
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| owner_facet | DE-824 DE-19 DE-BY-UBM DE-384 DE-29T DE-634 DE-83 DE-11 DE-188 |
| physical | XIV, 591 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Problem books in mathematics |
| spelling | De Souza, Paulo Ney Verfasser (DE-588)120560542 aut Berkeley problems in mathematics Paulo Ney de Souza ; Jorge-Nuno Silva 3. ed. New York [u.a.] Springer 2004 XIV, 591 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problem books in mathematics Literaturverz. S. 581 - 587 University of California, Berkeley. Dept. of Mathematics Examinations University of California Berkeley (DE-588)2025100-2 gnd rswk-swf Matemática (problemas e exercícios) larpcal Mathematik Mathematics Problems, exercises, etc Algebra (DE-588)4001156-2 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Mathematikstudium (DE-588)4037947-4 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Analysis (DE-588)4001865-9 s DE-604 Algebra (DE-588)4001156-2 s University of California Berkeley (DE-588)2025100-2 b Mathematikstudium (DE-588)4037947-4 s 1\p DE-604 Silva, Jorge-Nuno Verfasser aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012859868&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 | De Souza, Paulo Ney Silva, Jorge-Nuno Berkeley problems in mathematics University of California, Berkeley. Dept. of Mathematics Examinations University of California Berkeley (DE-588)2025100-2 gnd Matemática (problemas e exercícios) larpcal Mathematik Mathematics Problems, exercises, etc Algebra (DE-588)4001156-2 gnd Analysis (DE-588)4001865-9 gnd Mathematikstudium (DE-588)4037947-4 gnd |
| subject_GND | (DE-588)2025100-2 (DE-588)4001156-2 (DE-588)4001865-9 (DE-588)4037947-4 (DE-588)4143389-0 |
| title | Berkeley problems in mathematics |
| title_auth | Berkeley problems in mathematics |
| title_exact_search | Berkeley problems in mathematics |
| title_full | Berkeley problems in mathematics Paulo Ney de Souza ; Jorge-Nuno Silva |
| title_fullStr | Berkeley problems in mathematics Paulo Ney de Souza ; Jorge-Nuno Silva |
| title_full_unstemmed | Berkeley problems in mathematics Paulo Ney de Souza ; Jorge-Nuno Silva |
| title_short | Berkeley problems in mathematics |
| title_sort | berkeley problems in mathematics |
| topic | University of California, Berkeley. Dept. of Mathematics Examinations University of California Berkeley (DE-588)2025100-2 gnd Matemática (problemas e exercícios) larpcal Mathematik Mathematics Problems, exercises, etc Algebra (DE-588)4001156-2 gnd Analysis (DE-588)4001865-9 gnd Mathematikstudium (DE-588)4037947-4 gnd |
| topic_facet | University of California, Berkeley. Dept. of Mathematics Examinations University of California Berkeley Matemática (problemas e exercícios) Mathematik Mathematics Problems, exercises, etc Algebra Analysis Mathematikstudium Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012859868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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