Advanced calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York, NY u.a.
New York, NY u.a.
1965
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | CONTENTS
FOR THE STUDENT v
PREFACE vii
chapter 1 SETS AND FUNCTIONS 1
1.1 Introduction 1
1.2 Geometry 2
1.3 Distance 9
1.4 Functions 15
1.5 Topological ideas 24
1.6 Order properties and the LUB property 34
1.7 Sequences of points 40
1.8 Real sequences 45
chapter 2 CONTINUITY 55
2.1 Introduction 55
2.2 Basic definitions 55
2.3 Approximation properties and uniform continuity 65
2.4 Properties of continuous functions 72
2.5 Limits of functions 76
xi
2.6 Discontinuities 82
2.7 Mean value theorems and L Hospital s rule 89
chapter 3 INTEGRATION 97
3.1 The definite integral 97
3.2 Evaluation of definite integrals 107
3.3 Taylor s theorem 124
3.4 Improper integrals 131
3.5 Set functions 151
chapter 4 CONVERGENCE 158
4.1 Infinite series 158
4.2 Uniform convergence 180
4.3 Power series 196
4.4 Improper integrals with a parameter 204
4.5 The Gamma function 213
chapter 5 DIFFERENTIATION 221
5.1 Transformations 221
5.2 Linear functions and transformations 229
5.3 The differential of a function 238
5.4 Differentiation of composite functions 250
5.5 Differentials of transformations 263
5.6 Inverses of functions of one variable 270
5.7 Inverses of transformations; 274
5.8 The implicit function theorems 283
5.9 Functional dependence 287
chapter 6 APPLICATIONS TO GEOMETRY
AND ANALYSIS 296
6.1 Transformations of multiple integrals 296
6.2 Curves and arc length 313
6.3 Surfaces and surface area 330
6.4 Extremal properties of functions of several variables 349
xii
chapter 7 DIFFERENTIAL GEOMETRY
AND VECTOR CALCULUS 366
7.1 Integrals over curves and surfaces 360
7.2 Differential forms 370
7.3 Vector analysis 390
7.4 The theorems of Green, Gauss, and Stokes 405
7.5 Independence of path, and exact differential forms 423
chapter 8 SPECIAL APPLICATIONS 437
8.1 Field theory 437
8.2 Calculus of variations 445
SUGGESTED READING 457
appendix I FOUNDATIONS OF THE REAL
NUMBER SYSTEM 461
appendix II APPLICATIONS OF MATHEMATICS 468
appendix III LOGIC AND SET THEORY 476
appendix IV FURTHER TOPICS IN ANALYSIS 481
appendix V INTRODUCTION TO COMPLEX
ANALYSIS 486
ANSWERS AND HINTS 495
LIST OF SYMBOLS 519
INDEX 521
xiii
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| spelling | Buck, Robert Creighton Verfasser aut Advanced calculus 2. ed. New York, NY u.a. New York, NY u.a. 1965 txt rdacontent n rdamedia nc rdacarrier Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Buck, Ellen F. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009207487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buck, Robert Creighton Advanced calculus Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4151278-9 |
| title | Advanced calculus |
| title_auth | Advanced calculus |
| title_exact_search | Advanced calculus |
| title_full | Advanced calculus |
| title_fullStr | Advanced calculus |
| title_full_unstemmed | Advanced calculus |
| title_short | Advanced calculus |
| title_sort | advanced calculus |
| topic | Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analysis Einführung |
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