Calculus and analysis: a combined approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXI, 671 S. graph. Darst. |
| ISBN: | 9780470617953 |
Internformat
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| 245 | 1 | 0 | |a Calculus and analysis |b a combined approach |c Horst R. Beyer |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2010 | |
| 300 | |a XXI, 671 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804143069149265920 |
|---|---|
| adam_text | Titel: Calculus and analysis
Autor: Beyer, Horst R.
Jahr: 2010
CONTENTS
Preface xi
0.1 Short Introduction xi
0.2 Introduction xii
0.2.1 Background xii
0.2.2 General Approach of the Text xiii
0.2.2.1 Motivational Parts xiv
0.2.2.2 Core Theoretical Parts xv
0.2.2.3 Parts Containing Examples and Problems xvi
0.2.3 Miscellaneous Aspects of the Approach xvii
0.2.4 Requirements of Applications xviii
0.2.5 Remarks on the Role of Abstraction in Natural Sciences xix
Acknowledgments xxi
1 Calculus I 1
1.1 A Sketch of the Development of Rigor in Calculus and Analysis 1
1.2 Basics 3
1.2.1 Elementary Mathematical Logic 3
Problems 10
vii
VIII CONTENTS
1.2.2 Sets 12
Problems 19
1.2.3 Maps 20
Problems 32
1.3 Limits and Continuous Functions 35
1.3.1 Limits of Real-Number Sequences 35
Problems 56
1.3.2 Continuous Functions 58
Problems 81
1.4 Differentiation 83
Problems 99
1.5 Applications of Differentiation 101
Problems 155
1.6 Riemann Integration 159
Problems 186
2 Calculus II 191
2.1 Techniques of Integration 191
2.1.1 Change of Variables 191
Problems 204
2.1.2 Integration by Parts 205
Problems 216
2.1.3 Partial Fractions 217
Problems 229
2.1.4 Approximate Numerical Calculation of Integrals 230
Problems 237
2.2 Improper Integrals 238
Problems 258
2.3 Series of Real Numbers 261
Problems 292
2.4 Series of Functions 293
Problems 338
2.5 Analytical Geometry and Elementary Vector Calculus 343
2.5.1 Metric Spaces 344
Problems 351
2.5.2 Vector Spaces 352
Problems 373
2.5.3 Conic Sections 375
CONTENTS IX
Problems 387
2.5.4 Polar Coordinates 388
Problems 394
2.5.5 Quadric Surfaces 395
Problems 401
2.5.6 Cylindrical and Spherical Coordinates 403
Problems 406
2.5.7 Limits in M 408
Problems 411
2.5.8 Paths in W 412
Problems 426
3 Calculus III 429
3.1 Vector-Valued Functions of Several Variables 429
Problems 444
3.2 Derivatives of Vector-Valued Functions of Several Variables 447
Problems 468
3.3 Applications of Differentiation 473
Problems 494
3.4 Integration of Functions of Several Variables 496
Problems 530
3.5 Vector Calculus 538
Problems 548
3.6 Generalizations of the Fundamental Theorem of Calculus 550
3.6.1 Green s Theorem 555
3.6.2 Stokes Theorem 569
3.6.3 Gauss Theorem 581
Problems 590
Appendix A 597
A. 1 Construction of the Real-Number System 597
A.2 The Lebesgue Criterion for Riemann Integrability 606
A.3 Properties of the Determinant 610
A.4 The Inverse Mapping Theorem 623
References 629
Index of Notation 635
Index of Terminology 637
X CONTENTS
Problem Solutions 645
|
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| indexdate | 2024-07-09T22:41:48Z |
| institution | BVB |
| isbn | 9780470617953 |
| language | English |
| lccn | 2009054417 |
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| publishDate | 2010 |
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| publisher | Wiley |
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| spelling | Beyer, Horst R. Verfasser aut Calculus and analysis a combined approach Horst R. Beyer Hoboken, NJ Wiley 2010 XXI, 671 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Calculus Textbooks HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020425998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beyer, Horst R. Calculus and analysis a combined approach Calculus Textbooks |
| title | Calculus and analysis a combined approach |
| title_auth | Calculus and analysis a combined approach |
| title_exact_search | Calculus and analysis a combined approach |
| title_full | Calculus and analysis a combined approach Horst R. Beyer |
| title_fullStr | Calculus and analysis a combined approach Horst R. Beyer |
| title_full_unstemmed | Calculus and analysis a combined approach Horst R. Beyer |
| title_short | Calculus and analysis |
| title_sort | calculus and analysis a combined approach |
| title_sub | a combined approach |
| topic | Calculus Textbooks |
| topic_facet | Calculus Textbooks |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020425998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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