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Calculus light:

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Bibliographic Details
Main Authors:	Friedman, Menahem (Author), Kandel, Abraham 1941- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2011
Series:	Intelligent systems reference library 9
Subjects:	Infinitesimalrechnung Lehrbuch
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XI, 299 S. graph. Darst. 24 cm
ISBN:	9783642178474 3642178472 9783642178481

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MARC


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Record in the Search Index

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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
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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
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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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work_keys_str_mv	AT friedmanmenahem calculuslight AT kandelabraham calculuslight

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