Holdings: Single variable calculus

Single variable calculus: a first step

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Bibliographic Details
Main Author:	Zou, Yunzhi (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2018]
Series:	De Gruyter textbook
Subjects:	Infinitesimalrechnung Lehrbuch
Online Access:	Inhaltsverzeichnis http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110524628&searchTitles=true Inhaltsverzeichnis
Physical Description:	X, 414 Seiten Illustrationen, Diagramme 24 cm
ISBN:	9783110524628 3110524627

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MARC


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adam_text	CONTENTS PREFACE * V 1 PREREQUISITES FOR CALCULUS * 1 1.1 OVERVIEW OF CALCULUS * 1 1.2 SETS AND NUMBERS * 6 1.2.1 SETS ----- 6 1.2.2 NUMBERS * 8 1.2.3 THE LEAST UPPER BOUND PROPERTY * 9 1.2.4 THE EXTENDED REAL NUMBER SYSTEM * 11 1.2.5 INTERVALS * 12 1.3 FUNCTIONS * 14 1.3.1 DEFINITION OF A FUNCTION * 14 1.3.2 GRAPH OF A FUNCTION * 17 1.3.3 SOME BASIC FUNCTIONS AND THEIR GRAPHS * 18 1.3.4 BUILDING NEW FUNCTIONS * 20 1.3.5 FUNDAMENTAL ELEMENTARY FUNCTIONS * 31 1.3.6 PROPERTIES OF FUNCTIONS * 32 1.4 EXERCISES * 37 2 LIMITS AND CONTINUITY * 41 2.1 RATES OF CHANGE AND DERIVATIVES * 41 2.2 LIMITS OF A FUNCTION * 42 2.2.1 DEFINITION OF A LIMIT * 42 2.2.2 PROPERTIES OF LIMITS OF FUNCTIONS * 49 2.2.3 LIMIT LAWS ----- 50 2.2.4 ONE-SIDED LIMITS * 55 2.2.5 LIMITS INVOLVING INFINITY AND ASYMPTOTES * 59 2.3 LIMITS OF SEQUENCES * 68 2.3.1 DEFINITIONS AND PROPERTIES * 68 2.3.2 SUBSEQUENCES * 77 2.4 SQUEEZE THEOREM AND CAUCHYS THEOREM 78 2.5 INFINITESIMAL FUNCTIONS AND ASYMPTOTIC FUNCTIONS 2.6 CONTINUOUS AND DISCONTINUOUS FUNCTIONS * 91 2.6.1 CONTINUITY AND DISCONTINUITY * 91 2.6.2 CONTINUOUS FUNCTIONS * 94 2.6.3 THEOREMS ON CONTINUOUS FUNCTIONS * 99 2.6.4 UNIFORM CONTINUITY * 107 2.7 SOME PROOFS IN CHAPTER 2 * 108 2.8 EXERCISES ----- 114 3 THE DERIVATIVE * 121 3.1 DERIVATIVE OF A FUNCTION AT A POINT * 121 3.1.1 INSTANTANEOUS RATES OF CHANGE AND DERIVATIVES REVISITED * 121 3.1.2 ONE-SIDED DERIVATIVES * 128 3.1.3 A FUNCTION MAY FAIL TO HAVE A DERIVATIVE AT A POINT * 129 3.2 DERIVATIVE AS A FUNCTION * 133 3.2.1 GRAPHING THE DERIVATIVE OF A FUNCTION * 134 3.2.2 DERIVATIVES OF SOME BASIC FUNCTIONS * 135 3.3 DERIVATIVE LAWS * 139 3.4 DERIVATIVE OF AN INVERSE FUNCTION * 143 3.5 DIFFERENTIATING A COMPOSITE FUNCTION - THE CHAIN RULE * 147 3.6 DERIVATIVES OF HIGHER ORDERS * 152 3.7 IMPLICIT DIFFERENTIATION * 154 3.8 FUNCTIONS DEFINED BY PARAMETRIC AND POLAR EQUATIONS * 159 3.8.1 FUNCTIONS DEFINED BY PARAMETRIC EQUATIONS * 159 3.8.2 POLAR CURVES * 163 3.9 RELATED RATES OF CHANGE * 166 3.10 THE TANGENT LINE APPROXIMATION AND THE DIFFERENTIAL * 167 3.10.1 LINEARIZATION * 167 3.10.2 DIFFERENTIALS * 170 3.11 DERIVATIVE RULES - SUMMARY * 174 3.12 EXERCISES * 175 4 APPLICATIONS OF THE DERIVATIVE * 181 4.1 EXTREME VALUES AND THE CANDIDATE THEOREM * 181 4.2 THE MEAN VALUE THEOREM * 188 4.3 MONOTONIE FUNCTIONS AND THE FIRST DERIVATIVE TEST * 196 4.3.1 MONOTONIE FUNCTIONS ----- 196 4.3.2 THE FIRST DERIVATIVE TEST ----- 199 4.4 EXTENDED MEAN VALUE THEOREM AND THE LHOEPITAL RULES 201 4.4.1 EXTENDED MEAN VALUE THEOREM * 201 4.4.2 THE INDETERMINATE FORMS OO-OO, AND OXOO * 203 4.5 TAYLORS THEOREM 209 4.5.1 THE ERROR ANALYSIS FOR THE LINEAR APPROXIMATION * 209 4.5.2 THE QUADRATIC APPROXIMATION * 210 4.5.3 TAYLORS THEOREM ----- 214 4.6 CONCAVE FUNCTIONS AND THE SECOND DERIVATIVE TEST 219 4.6.1 CONCAVE FUNCTIONS * 219 4.6.2 THE SECOND DERIVATIVE TEST * 225 4.7 EXTREME VALUES OF FUNCTIONS REVISITED * 227 4.8 CURVE SKETCHING * 231 4.9 SOLVING EQUATIONS NUMERICALLY * 234 4.9.1 DECIMAL SEARCH * 234 4.9.2 NEWTONS METHOD ----- 236 4.10 CURVATURES AND THE DIFFERENTIAL OF THE ARC LENGTH 238 4.11 EXERCISES ----- 243 5 THE DEFINITE INTEGRAL * 249 5.1 DEFINITE INTEGRALS AND PROPERTIES * 249 5.1.1 INTRODUCTION ----- 249 5.1.2 PROPERTIES OF THE DEFINITE INTEGRAL * 259 5.1.3 INTERPRETING J^F(X)DX IN TERMS OF AREA * 265 5.1.4 INTERPRETING V(T) DT AS A DISTANCE OR DISPLACEMENT * 267 5.2 THE FUNDAMENTAL THEOREM OF CALCULUS * 267 5.3 NUMERICAL INTEGRATION * 275 5.3.1 TRAPEZOIDAL RULE * 276 5.3.2 SIMPSONS RULE ----- 277 5.4 EXERCISES 279 6 TECHNIQUES FOR INTEGRATION AND IMPROPER INTEGRALS * 285 6.1 INDEFINITE INTEGRALS * 285 6.1.1 DEFINITION OF INDEFINITE INTEGRALS AND BASIC ANTIDERIVATIVES * 285 6.1.2 DIFFERENTIAL EQUATIONS * 289 6.1.3 SUBSTITUTION IN INDEFINITE INTEGRALS * 293 6.1.4 FURTHER RESULTS USING INTEGRATION BY SUBSTITUTION * 297 6.1.5 INTEGRATION BY PARTS * 300 6.1.6 PARTIAL FRACTIONS IN INTEGRATION * 304 6.1.7 RATIONALIZING SUBSTITUTIONS * 312 6.2 SUBSTITUTION IN DEFINITE INTEGRALS * 313 6.3 INTEGRATION BY PARTS IN DEFINITE INTEGRALS * 317 6.4 IMPROPER INTEGRALS * 318 6.4.1 IMPROPER INTEGRALS OF THE FIRST KIND * 318 6.4.2 IMPROPER INTEGRALS OF THE SECOND KIND * 322 6.5 EXERCISES ----- 326 7 APPLICATIONS OF THE DEFINITE INTEGRAL * 333 7.1 AREAS, VOLUMES, AND ARC LENGTHS * 333 7.1.1 THE AREA OF THE REGION BETWEEN TWO CURVES * 333 7.1.2 VOLUMES OF SOLIDS ----- 337 7.1.3 ARC LENGTH * 339 7.2 APPLICATIONS IN OTHER DISCIPLINES * 344 7.2.1 DISPLACEMENT AND DISTANCE * 344 7.2.2 WORK DONE BY A FORCE ----- 345 7.2.3 FLUID PRESSURE * 346 7.2.4 CENTER OF MASS * 347 7.2.5 PROBABILITY ----- 349 7.3 EXERCISES * 350 8 INFINITE SERIES, SEQUENCES, AND APPROXIMATIONS * 355 8.1 INFINITE SEQUENCES * 355 8.2 INFINITE SERIES * 357 8.2.1 DEFINITION OF INFINITE SERIES * 357 8.2.2 PROPERTIES OF CONVERGENT SERIES * 359 8.3 TESTS FOR CONVERGENCE * 363 8.3.1 SERIES WITH NONNEGATIVE TERMS * 363 8.3.2 SERIES WITH NEGATIVE AND POSITIVE TERMS * 371 8.4 POWER SERIES AND TAYLOR SERIES * 375 8.4.1 POWER SERIES * 375 8.4.2 WORKING WITH POWER SERIES * 381 8.4.3 TAYLOR SERIES * 383 8.4.4 APPLICATIONS OF POWER SERIES * 391 8.5 FOURIER SERIES * 393 8.5.1 FOURIER SERIES EXPANSION WITH PERIOD 2 N * 394 8.5.2 FOURIER COSINE AND SINE SERIES WITH PERIOD 2N * 399 8.5.3 THE FOURIER SERIES EXPANSION WITH PERIOD 21 * 400 8.5.4 FOURIER SERIES WITH COMPLEX TERMS * 403 8.6 EXERCISES * 404 INDEX * 411
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author	Zou, Yunzhi
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spelling	Zou, Yunzhi Verfasser (DE-588)1155862910 aut Single variable calculus a first step Yunzhi Zou Berlin ; Boston De Gruyter [2018] X, 414 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-052785-8 Erscheint auch als Online-Ausgabe, PDF 978-3-11-052778-0 B:DE-101 application/pdf http://d-nb.info/1137843918/04 Inhaltsverzeichnis X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110524628&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030350025&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Zou, Yunzhi Single variable calculus a first step Infinitesimalrechnung (DE-588)4072798-1 gnd
subject_GND	(DE-588)4072798-1 (DE-588)4123623-3
title	Single variable calculus a first step
title_auth	Single variable calculus a first step
title_exact_search	Single variable calculus a first step
title_full	Single variable calculus a first step Yunzhi Zou
title_fullStr	Single variable calculus a first step Yunzhi Zou
title_full_unstemmed	Single variable calculus a first step Yunzhi Zou
title_short	Single variable calculus
title_sort	single variable calculus a first step
title_sub	a first step
topic	Infinitesimalrechnung (DE-588)4072798-1 gnd
topic_facet	Infinitesimalrechnung Lehrbuch
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