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Working analysis:

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Bibliographische Detailangaben
Beteilige Person:	Cooper, Jeffery (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Amsterdam [u.a.] Elsevier Acad. Press 2005
Schlagwörter:	Analysis
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017440056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVI, 663 S. graph. Darst.
ISBN:	0121876047

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Datensatz im Suchindex

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adam_text	WORKING ANALYSIS JEFFERY COOPER DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND AT COLLEGE PARK ELSEVIER AMSTERDAM BOSTON * HEIDELBERG * LONDON ACADEMIC N E W YORK * O X F O R D * PARIS * SAN DIEGO PRESS SAN FRANCISCO * SINGAPORE * SYDNEY * TOKYO CONTENTS PREFACE XI PARTI CHAPTER I FOUNDATIONS 3 1.1 ORDERED FIELDS 3 1.2 COMPLETENESS 8 1.3 USING INEQUALITIES 13 1.4 INDUCTION 19 1.5 SETS AND FUNCTIONS 22 CHAPTER 2 SEQUENCES OF REAL NUMBERS 29 2.1 LIMITS OF SEQUENCES 29 2.2 CRITERIA FOR CONVERGENCE 41 2.3 CAUCHY SEQUENCES 51 CHAPTER 3 CONTINUITY 57 3.1 LIMITS OF FUNCTIONS 57 3.2 CONTINUOUS FUNCTIONS 65 3.3 FURTHER PROPERTIES OF CONTINUOUS FUNCTIONS 70 V VI CONTENTS 3.4 GOLDEN-SECTION SEARCH 75 3.5 THE INTERMEDIATE VALUE THEOREM 80 CHAPTER 4 THE DERIVATIVE 85 4.1 THE DERIVATIVE AND APPROXIMATION S 85 4.2 THE MEAN VALUE THEOREM 96 4.3 THE CAUCHY MEAN VALUE THEOREM AND L HOPITAL S RULE 109 4.4 THE SECOND DERIVATIVE TEST 115 CHAPTER 5 HIGHER DERIVATIVES AND POLYNOMIAL APPROXIMATION 121 5.1 TAYLOR POLYNOMIALS 121 5.2 NUMERICAL DIFFERENTIATION 135 5.3 POLYNOMIAL INTERPOLATION 139 5.4 CONVEX FUNCTIONS 146 CHAPTER 6 SOLVING EQUATIONS IN ONE DIMENSION 151 6.1 FIXED POINT PROBLEMS 151 6.2 COMPUTATION WITH FUNCTIONAL ITERATION 158 6.3 NEWTON S METHOD 162 CHAPTER 7 INTEGRATION 171 7.1 THE DEFINITION OF THE INTEGRAL 171 7.2 PROPERTIES OF THE INTEGRAL 180 7.3 THE FUNDAMENTAL THEOREM OF CALCULUS AND FURTHER PROPERTIES OF THE INTEGRAL 189 7.4 NUMERICAL METHODS OF INTEGRATION 199 7.5 IMPROPER INTEGRALS 210 CONTENTS VII CHAPTER 8 SERIES 219 8.1 INFINITE SERIES 219 8.2 SEQUENCES AND SERIES OF FUNCTIONS ~ 230 8.3 POWER SERIES AND ANALYTIC FUNCTIONS 245 APPENDIX I 261 1.1 THE LOGARITHM FUNCTIONS AND EXPONENTIAL FUNCTIONS 261 1.2 THE TRIGONOMETRIC FUNCTIONS 265 PART II CHAPTER 9 CONVERGENCE AND CONTINUITY IN R 271 9.1 NORMS 272 9.2 A LITTLE TOPOLOGY 278 9.3 CONTINUOUS FUNCTIONS OF SEVERAL VARIABLES 286 CHAPTER 10 THE DERIVATIVE IN W 1 295 10.1 THE DERIVATIVE AND APPROXIMATION IN R 295 10.2 LINEAR TRANSFORMATIONS AND MATRIX NORMS 306 10.3 VECTOR-VALUED MAPPINGS 310 CHAPTER I I SOLVING SYSTEMS OF EQUATIONS 323 11.1 LINEAR SYSTEMS 324 11.2 THE CONTRACTION MAPPING THEOREM V 326 11.3 NEWTON S METHOD 333 11.4 THE INVERSE FUNCTION THEOREM 347 11.5 THE IMPLICIT FUNCTION THEOREM 359 11.6 AN APPLICATION IN MECHANICS 373 VIII CONTENTS CHAPTER 12 QUADRATIC APPROXIMATION AND OPTIMIZATION 385 12.1 HIGHER DERIVATIVES AND QUADRATIC APPROXIMATION 386 12.2 CONVEX FUNCTIONS 397 12.3 POTENTIALS AND DYNAMICAL SYSTEMS 402 12.4 THE METHOD OF STEEPEST DESCENT 410 12.5 CONJUGATE GRADIENT METHODS 417 12.6 SOME OPTIMIZATION PROBLEMS 427 CHAPTER 13 CONSTRAINED OPTIMIZATION 439 13.1 LAGRANGE MULTIPLIERS 439 13.2 DEPENDENCE ON PARAMETERS AND SECOND-ORDER CONDITIONS 454 13.3 CONSTRAINED OPTIMIZATION WITH INEQUALITIES 468 13.4 APPLICATIONS IN ECONOMICS 474 CHAPTER 14 INTEGRATION IN E 489 14.1 INTEGRATION OVER GENERALIZED RECTANGLES 489 14.2 INTEGRATION OVER JORDAN DOMAINS 496 14.3 NUMERICAL METHODS 504 14.4 CHANGE OF VARIABLE IN MULTIPLE INTEGRALS 514 14.5 APPLICATIONS OF THE CHANGE OF VARIABLE THEOREM 524 14.6 IMPROPER INTEGRALS IN SEVERAL VARIABLES 536 14.7 APPLICATIONS IN PROBABILITY 545 CHAPTER 15 APPLICATIONS OF INTEGRATION TO DIFFERENTIAL EQUATIONS 555 15.1 INTERCHANGING LIMITS AND INTEGRALS 555 15.2 APPROXIMATION BY SMOOTH FUNCTIONS 567 15.3 DIFFUSION 578 15.4 FLUID FLOW 587 CONTENTS * APPENDIX II 599 A MATRIX FACTORIZATION 599 SOLUTIONS TO SELECTED EXERCISES 603 REFERENCES 631 INDEX 633
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