Real analysis with real applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Prentice Hall
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Spätere Ausg. u.d.T.: Davidson, Kenneth R.: Real analysis and applications |
| Physical Description: | XVII, 624 S. graph. Darst. |
| ISBN: | 0130416479 |
Staff View
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Record in the Search Index
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| adam_text | REAL ANALYSIS WITH REAL APPLICATIONS KENNETH R. DAVIDSON UNIVERSITY OF
WATERLOO ALLAN P. DONSIG UNIVERSITY OF NEBRASKA PRENTICE HALL PRENTICE
HALL UPPER SADDLE RIVER, NJ 07458 CONTENTS PREFACE XI DEPENDENCE ON
EARLIER SECTIONS XIV POSSIBLE COURSE OUTLINES XVI 1 BACKGROUND 1 1.1 THE
LANGUAGE OF MATHEMATICS 1 1.2 SETS AND FUNCTIONS 5 1.3 CALCULUS 10 1.4
LINEAR ALGEBRA 11 1.5 THE ROLE OF PROOFS 19 * 1.6 APPENDIX: EQUIVALENCE
RELATIONS 25 PART A ABSTRACT ANALYSIS 29 2 THE REAL NUMBERS 31 2.1 AN
OVERVIEW OF THE REAL NUMBERS 31 2.2 INFINITE DECIMALS 34 2.3 LIMITS 37
2.4 BASIC PROPERTIES OF LIMITS 42 2.5 UPPER AND LOWER BOUNDS 46 2.6
SUBSEQUENCES 51 2.7 CAUCHY SEQUENCES 55 * 2.8 APPENDIX: CARDINALITY 60 3
SERIES 66 3.1 CONVERGENT SERIES 66 3.2 CONVERGENCE TESTS FOR SERIES 70 *
3.3 THE NUMBER E - 77 * 3.4 ABSOLUTE AND CONDITIONAL CONVERGENCE 80 4
THE TOPOLOGY OF R N 88 4.1 N-DIMENSIONAL SPACE 88 4.2 CONVERGENCE AND
COMPLETENESS IN R N 92 4.3 CLOSED AND OPEN SUBSETS OF R N 96 4.4 COMPACT
SETS AND THE HEINE-BOREL THEOREM 101 VIII CONTENTS 5 5.1 5.2 5.3 5.4 5.5
5.6 * 5.7 6 6.1 6.2 6.3 6.4 * 6.5 *6.6 7 7.1 7.2 7.3 7.4 * 7.5 * 7.6 *
7.7 8 8.1 8.2 8.3 8.4 * 8.5 * 8.6 9 9.1 * 9.2 * 9.3 * 9.4 * 9.5 * 9.6
FUNCTIONS LIMITS AND CONTINUITY DISCONTINUOUS FUNCTIONS PROPERTIES OF
CONTINUOUS FUNCTIONS COMPACTNESS AND EXTREME VALUES UNIFORM CONTINUITY
THE INTERMEDIATE VALUE THEOREM MONOTONE FUNCTIONS DIFFERENTIATION AND
INTEGRATION DIFFERENTIABLE FUNCTIONS THE MEAN VALUE THEOREM RIEMANN
INTEGRATION THE FUNDAMENTAL THEOREM OF CALCULUS WALLIS S PRODUCT AND
STIRLING S FORMULA MEASURE ZERO AND LEBESGUE S THEOREM NORMED VECTOR
SPACES DEFINITION AND EXAMPLES TOPOLOGY IN NORMED SPACES INNER PRODUCT
SPACES ORTHONORMAL SETS ORTHOGONAL EXPANSIONS IN INNER PRODUCT SPACES
FINITE-DIMENSIONAL NORMED SPACES THE IP NORMS LIMITS OF FUNCTIONS LIMITS
OF FUNCTIONS UNIFORM CONVERGENCE AND CONTINUITY UNIFORM CONVERGENCE AND
INTEGRATION SERIES OF FUNCTIONS POWER SERIES COMPACTNESS AND SUBSETS OF
C(K) METRIC SPACES DEFINITIONS AND EXAMPLES COMPACT METRIC SPACES
COMPLETE METRIC SPACES CONNECTEDNESS METRIC COMPLETION THE LP SOACES AND
ABSTRACT INTEGRATION 108 108 114 120 124 127 133 135 141 141 148 153 164
169 175 179 179 184 187 191 196 204 208 213 213 218 220 225 232 239 246
246 250 254 257 261 266 CONTENTS IX PART B APPLICATIONS 273 10
APPROXIMATION BY POLYNOMIALS 275 10.1 TAYLOR SERIES 275 10.2 HOW NOT TO
APPROXIMATE A FUNCTION 285 10.3 BERNSTEIN S PROOF OF THE WEIERSTRASS
THEOREM 290 10.4 ACCURACY OF APPROXIMATION 294 * 10.5 EXISTENCE OF BEST
APPROXIMATIONS 297 * 10.6 CHARACTERIZING BEST APPROXIMATIONS 300 * 10.7
EXPANSIONS USING CHEBYCHEV POLYNOMIALS 306 * 10.8 SPLINES 314 * 10.9
UNIFORM APPROXIMATION BY SPLINES 322 * 10.10 APPENDIX: THE
STONE-WEIERSTRASS THEOREM 326 11 DISCRETE DYNAMICAL SYSTEMS 331 11.1 ,.
FIXED POINTS AND THE CONTRACTION PRINCIPLE 332 11.2 NEWTON S METHOD 344
* 11.3 ORBITS OF A DYNAMICAL SYSTEM 349 * 11.4 PERIODIC POINTS 355 *
11.5 CHAOTIC SYSTEMS 362 * 11.6 TOPOLOGICAL CONJUGACY 370 * 11.7
ITERATED FUNCTION SYSTEMS AND FRACTALS 378 12 DIFFERENTIAL EQUATIONS 386
12.1 INTEGRAL EQUATIONS AND CONTRACTIONS 386 12.2 CALCULUS OF
VECTOR-VALUED FUNCTIONS 390 12.3 DIFFERENTIAL EQUATIONS AND FIXED POINTS
395 12.4 SOLUTIONS OF DIFFERENTIAL EQUATIONS 399 12.5 LOCAL SOLUTIONS
405 * 12.6 LINEAR DIFFERENTIAL EQUATIONS 411 * 12.7 PERTURBATION AND
STABILITY OF DES 416 * 12.8 EXISTENCE WITHOUT UNIQUENESS 420 13 FOURIER
SERIES AND PHYSICS 423 * 13.1 THE STEADY-STATE HEAT EQUATION 423 13.2
FORMAL SOLUTION 427 13.3 ORTHOGONALITY RELATIONS 429 13.4 CONVERGENCE IN
THE OPEN DISK 432 13.5 THE POISSON FORMULA 435 13.6 POISSON S THEOREM
439 13.7 THE MAXIMUM PRINCIPLE 443 * 13.8 THE VIBRATING STRING (FORMAL
SOLUTION) 446 * 13.9 THE VIBRATING STRING (RIGOUROUS SOLUTION) 450 *
13.10 APPENDIX: THE COMPLEX EXPONENTIAL 454 X CONTENTS 14 FOURIER SERIES
AND APPROXIMATION 463 14.1 LEAST SQUARES APPROXIMATIONS 463 * 14.2 THE
ISOPERIMETRIC PROBLEM 468 14.3 THE RIEMANN-LEBESGUE LEMMA 471 14.4
POINTWISE CONVERGENCE OF FOURIER SERIES 476 * 14.5 GIBBS S PHENOMENON
485 14.6 CESARO SUMMATION OF FOURIER SERIES 488 * 14.7 BEST
APPROXIMATION BY TRIG POLYNOMIALS 495 * 14.8 CONNECTIONS WITH POLYNOMIAL
APPROXIMATION 498 * 14.9 JACKSON S THEOREM AND BERNSTEIN S THEOREM 503
15 WAVELETS 513 15.1 INTRODUCTION 513 15.2 THE HAAR WAVELET 515 15.3
MULTIRESOLUTION ANALYSIS 520 15.4 RECOVERING THE WAVELET 524 * 15.5
DAUBECHIES WAVELETS 528 * 15.6 EXISTENCE OF THE DAUBECHIES WAVELETS 534
* 15.7 APPROXIMATIONS USING WAVELETS 537 * 15.8 THE FRANKLIN WAVELET 541
* 15.9 RIESZ MULTIRESOLUTION ANALYSIS 548 16 CONVEXITY AND OPTIMIZATION
557 16.1 CONVEX SETS 557 16.2 RELATIVE INTERIOR 564 16.3 SEPARATION
THEOREMS 568 16.4 EXTREME POINTS 573 16.5 CONVEX FUNCTIONS IN ONE
DIMENSION 576 * 16.6 CONVEX FUNCTIONS IN HIGHER DIMENSIONS 583 * 16.7
SUBDIFFERENTIALS AND DIRECTIONAL DERIVATIVES 587 * 16.8 TANGENT AND
NORMAL CONES 596 * 16.9 CONSTRAINED MINIMIZATION 601 * 16.10 THE MINIMAX
THEOREM 608 REFERENCES 615 INDEX 617
|
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| author | Davidson, Kenneth R. 1951- Donsig, Allan P. |
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| indexdate | 2024-07-09T19:00:25Z |
| institution | BVB |
| isbn | 0130416479 |
| language | English |
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| spelling | Davidson, Kenneth R. 1951- Verfasser (DE-588)139971599 aut Real analysis with real applications Kenneth R. Davidson ; Allan P. Donsig Upper Saddle River, NJ Prentice Hall 2002 XVII, 624 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Spätere Ausg. u.d.T.: Davidson, Kenneth R.: Real analysis and applications Analyse mathématique Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 s DE-604 Donsig, Allan P. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009773198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davidson, Kenneth R. 1951- Donsig, Allan P. Real analysis with real applications Analyse mathématique Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 |
| title | Real analysis with real applications |
| title_auth | Real analysis with real applications |
| title_exact_search | Real analysis with real applications |
| title_full | Real analysis with real applications Kenneth R. Davidson ; Allan P. Donsig |
| title_fullStr | Real analysis with real applications Kenneth R. Davidson ; Allan P. Donsig |
| title_full_unstemmed | Real analysis with real applications Kenneth R. Davidson ; Allan P. Donsig |
| title_short | Real analysis with real applications |
| title_sort | real analysis with real applications |
| topic | Analyse mathématique Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Analyse mathématique Mathematical analysis Reelle Analysis |
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