Berkeley problems in mathematics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Problem books in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 535 S. graph. Darst. |
| ISBN: | 0387951849 0387952071 |
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 DeSouza ; Jorge-Nuno Silva |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XIV, 535 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 | |
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Datensatz im Suchindex
| _version_ | 1822490863271411712 |
|---|---|
| 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 13
1.5 Integral Calculus 17
1.6 Sequences of Functions 21
1.7 Fourier Series 26
1.8 Convex Functions 28
2 Multivariable Calculus 29
2.1 Limits and Continuity 29
2.2 Differential Calculus 30
2.3 Integral Calculus 37
3 Differential Equations 41
3.1 First Order Equations 41
3.2 Second Order Equations 45
xii Contents
3.3 Higher Order Equations 47
3.4 Systems of Differential Equations 48
4 Metric Spaces 53
4.1 Topology of M" 53
4.2 General Theory 56
4.3 Fixed Point Theorem 57
5 Complex Analysis 59
5.1 Complex Numbers 59
5.2 Series and Sequences of Functions 61
5.3 Conformal Mappings 64
5.4 Functions on the Unit Disc 65
5.5 Growth Conditions 67
5.6 Analytic and Meromorphic Functions 68
5.7 Cauchy's Theorem 73
5.8 Zeros and Singularities 75
5.9 Harmonic Functions 78
5.10 Residue Theory 79
5.11 Integrals Along the Real Axis 85
6 Algebra 89
6.1 Examples of Groups and General Theory 89
6.2 Homomorphisms and Subgroups 91
6.3 Cyclic Groups 93
6.4 Normality, Quotients, and Homomorphisms 94
6.5 Sn,An,Dn, 96
6.6 Direct Products 97
6.7 Free Groups, Generators, and Relations 98
6.8 Finite Groups 99
6.9 Rings and Their Homomorphisms 100
6.10 Ideals 101
6.11 Polynomials 103
6.12 Fields and Their Extensions 106
6.13 Elementary Number Theory 108
7 Linear Algebra 111
7.1 Vector Spaces Ill
7.2 Rank and Determinants 113
7.3 Systems of Equations 116
7.4 Linear Transformations 116
7.5 Eigenvalues and Eigenvectors 120
7.6 Canonical Forms 125
7.7 Similarity 130
7.8 Bilinear, Quadratic Forms, and Inner Product Spaces 132
Contents xiii
7.9 General Theory of Matrices 135
II Solutions 141
1 Real Analysis 143
1.1 Elementary Calculus 143
1.2 Limits and Continuity 158
1.3 Sequences, Series, and Products 163
1.4 Differential Calculus 175
1.5 Integral Calculus 184
1.6 Sequences of Functions 196
1.7 Fourier Series 208
1.8 Convex Functions 212
2 Multivariable Calculus 215
2.1 Limits and Continuity 215
2.2 Differential Calculus 217
2.3 Integral Calculus 236
3 Differential Equations 243
3.1 First Order Equations 243
3.2 Second Order Equations 252
3.3 Higher Order Equations 256
3.4 Systems of Differential Equations 257
4 Metric Spaces 269
4.1 Topology of E" 269
4.2 General Theory 276
4.3 Fixed Point Theorem 279
5 Complex Analysis 283
5.1 Complex Numbers 283
5.2 Series and Sequences of Functions 287
5.3 Conformal Mappings 293
5.4 Functions on the Unit Disc 297
5.5 Growth Conditions 305
5.6 Analytic and Meromorphic Functions 309
5.7 Cauchy's Theorem 321
5.8 Zeros and Singularities 330
5.9 Harmonic Functions 345
5.10 Residue Theory 347
5.11 Integrals Along the Real Axis 362
6 Algebra 391
6.1 Examples of Groups and General Theory 391
xiv Contents
6.2 Homomorphisms and Subgroups 396
6.3 Cyclic Groups 399
6.4 Normality, Quotients, and Homomorphisms 400
6.5 Sn,An,Dn, 404
6.6 Direct Products 406
6.7 Free Groups, Generators, and Relations 408
6.8 Finite Groups 413
6.9 Rings and Their Homomorphisms 417
6.10 Ideals 420
6.11 Polynomials 424
6.12 Fields and Their Extensions 431
6.13 Elementary Number Theory 436
7 Linear Algebra 443
7.1 Vector Spaces 443
7.2 Rank and Determinants 449
7.3 Systems of Equations 454
7.4 Linear Transformations 455
7.5 Eigenvalues and Eigenvectors 465
7.6 Canonical Forms 474
7.7 Similarity 487
7.8 Bilinear, Quadratic Forms, and Inner Product Spaces 491
7.9 General Theory of Matrices 500
III Appendices 513
A How to Get the Exams 515
A.I On line 515
A.2 Off line, the Last Resort 515
B Passing Scores 521
C The Syllabus 523
References 525
Index 533 |
| 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 | BV013839870 |
| callnumber-first | Q - Science |
| callnumber-label | QA43 |
| callnumber-raw | QA43.D38 2001 |
| callnumber-search | QA43.D38 2001 |
| callnumber-sort | QA 243 D38 42001 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 |
| classification_tum | MAT 580f MAT 080f |
| ctrlnum | (OCoLC)248494111 (DE-599)BVBBV013839870 |
| dewey-full | 515/.076 515/.07621 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.076 515/.076 21 |
| dewey-search | 515/.076 515/.076 21 |
| dewey-sort | 3515 276 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2025-01-28T11:12:07Z |
| institution | BVB |
| isbn | 0387951849 0387952071 |
| language | English |
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| spelling | De Souza, Paulo Ney Verfasser (DE-588)120560542 aut Berkeley problems in mathematics Paulo Ney DeSouza ; Jorge-Nuno Silva 2. ed. New York [u.a.] Springer 2001 XIV, 535 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problem books in mathematics University of California, Berkeley - Dept. of Mathematics - Examens University of California, Berkeley. Dept. of Mathematics -- Examinations University of California Berkeley (DE-588)2025100-2 gnd rswk-swf Fonctions d'une variable complexe ram Fonctions réelles ram Mathématiques - Examens, questions, etc Mathématiques - Problèmes et exercices ram Wiskunde gtt Équations différentielles ram Mathematik Mathematics -- Examinations, questions, 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 University of California Berkeley (DE-588)2025100-2 b Mathematikstudium (DE-588)4037947-4 s DE-604 Analysis (DE-588)4001865-9 s Algebra (DE-588)4001156-2 s Silva, Jorge-Nuno Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009466674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Souza, Paulo Ney Silva, Jorge-Nuno Berkeley problems in mathematics University of California, Berkeley - Dept. of Mathematics - Examens University of California, Berkeley. Dept. of Mathematics -- Examinations University of California Berkeley (DE-588)2025100-2 gnd Fonctions d'une variable complexe ram Fonctions réelles ram Mathématiques - Examens, questions, etc Mathématiques - Problèmes et exercices ram Wiskunde gtt Équations différentielles ram Mathematik Mathematics -- Examinations, questions, 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 DeSouza ; Jorge-Nuno Silva |
| title_fullStr | Berkeley problems in mathematics Paulo Ney DeSouza ; Jorge-Nuno Silva |
| title_full_unstemmed | Berkeley problems in mathematics Paulo Ney DeSouza ; Jorge-Nuno Silva |
| title_short | Berkeley problems in mathematics |
| title_sort | berkeley problems in mathematics |
| topic | University of California, Berkeley - Dept. of Mathematics - Examens University of California, Berkeley. Dept. of Mathematics -- Examinations University of California Berkeley (DE-588)2025100-2 gnd Fonctions d'une variable complexe ram Fonctions réelles ram Mathématiques - Examens, questions, etc Mathématiques - Problèmes et exercices ram Wiskunde gtt Équations différentielles ram Mathematik Mathematics -- Examinations, questions, 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 - Examens University of California, Berkeley. Dept. of Mathematics -- Examinations University of California Berkeley Fonctions d'une variable complexe Fonctions réelles Mathématiques - Examens, questions, etc Mathématiques - Problèmes et exercices Wiskunde Équations différentielles Mathematik Mathematics -- Examinations, questions, etc Algebra Analysis Mathematikstudium Aufgabensammlung |
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