Calculus light:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Intelligent systems reference library
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 299 S. graph. Darst. 24 cm |
| ISBN: | 9783642178474 3642178472 9783642178481 |
Internformat
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Datensatz im Suchindex
| _version_ | 1805096157073899520 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 HISTORICAL BACKGROUND 1
1.1 PRELUDE TO CALCULUS OR THE TERROR OF THE 'INFINITE' 1
1.2 CALCULUS - WHERE DO WE START? 2
1.3 THE COUNTDOWN 5
1.4 THE BIRTH OF CALCULUS 6
1.5 THE PRIORITY DISPUTE 8
2 THE NUMBER SYSTEM 11
2.1 BASIC CONCEPTS ABOUT SETS 11
2.2 THE NATURAL NUMBERS 14
2.3 INTEGERS AND RATIONAL NUMBERS 17
2.3.1 INTEGERS 18
2.3.2 RATIONAL NUMBERS 19
2.4 REAL NUMBERS 22
2.5 ADDITIONAL PROPERTIES OF THE REAL NUMBERS 30
3 FUNCTIONS, SEQUENCES AND LIMITS 37
3.1 INTRODUCTION 37
3.2 FUNCTIONS 39
3.3 ALGEBRAIC FUNCTIONS 48
3.4 SEQUENCES 55
3.5 BASIC LIMIT THEOREMS 62
3.6 LIMIT POINTS 70
3.7 SPECIAL SEQUENCES 74
3.7.1 MONOTONE SEQUENCES 75
3.7.2 CONVERGENCE TO INFINITY 77
3.7.3 CAUCHY SEQUENCES 82
4 CONTINUOUS FUNCTIONS 87
4.1 LIMITS OF FUNCTIONS 87
4.2 CONTINUITY 89
4.3 PROPERTIES OF CONTINUOUS FUNCTIONS 94
4.4 CONTINUITY OF SPECIAL FUNCTIONS 98
4.5 UNIFORM CONTINUITY 104
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009481096
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
5 DIFFERENTIABLE FUNCTIONS 107
5.1 A DERIVATIVE OF A FUNCTION 107
5.2 BASIC PROPERTIES OF DIFFERENTIABLE FUNCTIONS 115
5.3 DERIVATIVES OF SPECIAL FUNCTIONS 125
5.4 HIGHER ORDER DERIVATIVES; TAYLOR'S THEOREM 131
5.5 L'HOSPITAL'S RULES 141
6 INTEGRATION 147
6.1 THERIEMANN INTEGRAL 147
6.2 INTEGRABLE FUNCTIONS 155
6.3 BASIC PROPERTIES OF THE RIEMANN INTEGRAL 158
6.4 THE FUNDAMENTAL THEOREM OF CALCULUS 166
6.5 THE MEAN-VALUE THEOREMS 171
6.6 METHODS OF INTEGRATION 175
6.7 IMPROPER INTEGRALS 179
7 INFINITE SERIES 183
7.1 CONVERGENCE 183
7.2 TESTS FOR CONVERGENCE 186
7.3 CONDITIONAL AND ABSOLUTE CONVERGENCE 193
7.4 MULTIPLICATION OF SERIES AND INFINITE PRODUCTS 203
7.5 POWER SERIES AND TAYLOR SERIES 210
8 FOURIER SERIES 217
8.1 TRIGONOMETRIC SERIES 217
8.2 CONVERGENCE 225
8.3 EVEN AND ODD FUNCTIONS 229
8.3.1 EVEN FUNCTIONS 229
8.3.2 ODD FUNCTIONS 230
9 ELEMENTARY NUMERICAL METHODS 233
9.1 INTRODUCTION 233
9.2 ITERATION 235
9.3 THE NEWTON - RAPHSON METHOD 242
9.4 INTERPOLATION METHODS 247
9.4.1 LAGRANGE POLYNOMIAL 247
9.4.2 CUBIC SPLINES 250
9.5 LEAST - SQUARES APPROXIMATIONS 252
9.5.1 LINEAR LEAST - SQUARES METHOD 253
9.5.2 QUADRATIC LEAST - SQUARES METHOD 254
9.6 NUMERICAL INTEGRATION 256
9.6.1 THE TRAPEZOIDAL RULE 256
9.6.2 SIMPSON RULE 257
9.6.3 GAUSSIAN INTEGRATION 259
IMAGE 3
CONTENTS XI
10 SPECIAL TOPICS 263
10.1 THE IRRATIONALITY OF E 263
10.2 EULER'S SUMMATION FORMULA 264
10.3 LAGRANGE MULTIPLIERS 270
10.3.1 INTRODUCTION: MULTI-VARIABLE FUNCTIONS 270
10.3.2 LAGRANGE MULTIPLIERS 274
SOLUTIONS TO SELECTED PROBLEM 283
INDEX 297 |
| any_adam_object | 1 |
| author | Friedman, Menahem Kandel, Abraham 1941- |
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| author_facet | Friedman, Menahem Kandel, Abraham 1941- |
| author_role | aut aut |
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| author_variant | m f mf a k ak |
| building | Verbundindex |
| bvnumber | BV037468192 |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)723413739 (DE-599)DNB1009481096 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037468192 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T11:10:42Z |
| institution | BVB |
| isbn | 9783642178474 3642178472 9783642178481 |
| language | English |
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| physical | XI, 299 S. graph. Darst. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Intelligent systems reference library |
| series2 | Intelligent systems reference library |
| spelling | Friedman, Menahem Verfasser aut Calculus light Menahem Friedman and Abraham Kandel Berlin [u.a.] Springer 2011 XI, 299 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Intelligent systems reference library 9 Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Kandel, Abraham 1941- Verfasser (DE-588)12865242X aut Intelligent systems reference library 9 (DE-604)BV035704685 9 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3607977&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022620008&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedman, Menahem Kandel, Abraham 1941- Calculus light Intelligent systems reference library Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4123623-3 |
| title | Calculus light |
| title_auth | Calculus light |
| title_exact_search | Calculus light |
| title_full | Calculus light Menahem Friedman and Abraham Kandel |
| title_fullStr | Calculus light Menahem Friedman and Abraham Kandel |
| title_full_unstemmed | Calculus light Menahem Friedman and Abraham Kandel |
| title_short | Calculus light |
| title_sort | calculus light |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Infinitesimalrechnung Lehrbuch |
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