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Analysis: a gateway to understanding mathematics

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Bibliographic Details
Main Author:	Dineen, Seán 1944- (Author)
Format:	Book
Language:	English
Published:	Singapore [u.a.] World Scientific 2012
Subjects:	Reelle Analysis
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Item Description:	Literaturverz. S. 291 - 293
Physical Description:	XVIII, 301 S. graph. Darst.
ISBN:	9814401382 9789814401388

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MARC


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Record in the Search Index

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adam_text	Contents PREFACE xi 1. QUADRATIC EQUATIONS 1 1.1 Quadratic Equations ..................... 1 1.2 Further Consequences ..................... 14 1.3 Exercises ............................ 19 2. DIAGRAMS 21 2.1 Graphs ............................. 21 2.2 Exercises ............................ 37 3. FUNCTIONS 39 3.1 Functions ............................ 39 3.2 Generating New Functions .................. 53 3.3 Exercises .........,,.,..,............ 57 4. INVERSE FUNCTIONS 59 4.1 Inject íve and Surjective Functions .............. 60 4.2 Bijective Functions and Inverses ............... 63 4.3 Increasing, Decreasing, Convex and Indicator Functions . . 69 4.4 Exercises ............................ 72 5. NUMBERS 77 5.1 The Positive Integers ..................... 77 5.2 The Integers and Rational Numbers ............. 85 5.3 Arithmetic and Geometry .................. 93 5.4 Exercises ............................ 101 6. SETS OF REAL NUMBERS 103 6.1 Countable Sets ......................... 103 6.2 Uncountable Sets ....................... 108 6.3 Sets Which Are Bounded Above ............... ПО 6.4 Intervals ............................ 114 6.5 Exercises ............................ 115 7. SERIES WITH POSITIVE ENTRIES 117 7.1 Increasing and Decreasing Sequences ............ 117 7.2 Series with Positive Entries .................. 124 7.3 The Exponential Function .................. 128 7.4 Multiplication of Series .................... 130 7.5 The Log Function ....................... 131 7.6 Exercises ............................ 135 8. REVIEW AND TRANSITION 137 8.1 Review and Preview ...................... 137 8.2 Convergent Sequences ..................... 139 8.3 Convergent Series ....................... 142 8.4 Power Series .......................... 148 8.5 Exercises ............................ 151 9. CONTINUOUS FUNCTIONS 155 9.1 Continuous Functions ..................... 155 9.2 Intermediate Value Theorem ................. 159 9.3 Fundamental Existence Theorem for Maxima and Minima 162 9.4 Exercises ............................ 166 10. DIFFERENTIABLE FUNCTIONS 169 10.1 DifFerentiable Functions.................... 169 10.2 Basic Functions and Rules for Differentiation ........ 174 10.3 Mean Value Theorem ..................... 177 10.4 Exercises ............................ 185 11. APPLICATIONS OF DIFFERENTIATION 189 11.1 Sequences ........................... 189 11.2 Limits ............................, 192 11.3 Curve Sketching ........................ 195 11.4 Applications of the Mean. Value Theorem .......... 201 11.5 In Retrospect ......................... 211 11.6 Exercises ............................ 213 12. THE REAL NUMBERS 219 12.1 Upper Bounds ......................... 219 12.2 Dyadic Sections and the Bisection Principle ........ 222 12.3 Foundational Developments ................. 229 12.4 Infinitesimals .......................... 234 12.5 Exercises ............................ 235 13. INTEGRATION THEORY 237 13.1 The Riemann Integral ..................... 23 Y 13.2 Fundamental Theorem or Calculus .............. 245 13.3 Methods of Integration .................... 24V 13.4 Exercises ........................, , , . 251 14. APPLICATIONS OF INTEGRATION THEORY 253 14.1 Integral Inequalities ...................... 254 14.2 Integrals over Infinite Intervals ................ 255 14.3 Taylor s Theorem ....................... 262 14.4 Exercises ............................ 265 SOL UTIONS 269 BIBLIOGRAPHY 291 INDEX 295
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author	Dineen, Seán 1944-
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dewey-full	510
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	510 - Mathematics
dewey-raw	510
dewey-search	510
dewey-sort	3510
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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id	DE-604.BV040539615
illustrated	Illustrated
indexdate	2024-07-10T00:26:05Z
institution	BVB
isbn	9814401382 9789814401388
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-025385555
oclc_num	820393552
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physical	XVIII, 301 S. graph. Darst.
publishDate	2012
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publisher	World Scientific
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spelling	Dineen, Seán 1944- Verfasser (DE-588)115656715 aut Analysis a gateway to understanding mathematics Seán Dineen Singapore [u.a.] World Scientific 2012 XVIII, 301 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 291 - 293 Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 s DE-604 DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/715469037.pdf Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025385555&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dineen, Seán 1944- Analysis a gateway to understanding mathematics Reelle Analysis (DE-588)4627581-2 gnd
subject_GND	(DE-588)4627581-2
title	Analysis a gateway to understanding mathematics
title_auth	Analysis a gateway to understanding mathematics
title_exact_search	Analysis a gateway to understanding mathematics
title_full	Analysis a gateway to understanding mathematics Seán Dineen
title_fullStr	Analysis a gateway to understanding mathematics Seán Dineen
title_full_unstemmed	Analysis a gateway to understanding mathematics Seán Dineen
title_short	Analysis
title_sort	analysis a gateway to understanding mathematics
title_sub	a gateway to understanding mathematics
topic	Reelle Analysis (DE-588)4627581-2 gnd
topic_facet	Reelle Analysis
url	http://www.gbv.de/dms/tib-ub-hannover/715469037.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025385555&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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