Continuous functions / (Record no. 89299)

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005 - DATE AND TIME OF LATEST TRANSACTION
control field 20241212124713.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION
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007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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fixed length control field 241212b ||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781786300102
Qualifying information (print)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781119332244
Qualifying information (electronic bk. : oBook)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 1119332249http://citulib.pinnacle.com.ph:8080/cgi-bin/koha/cataloguing/addbiblio.pl?biblionumber=89299#
Qualifying information (electronic bk. : oBook)
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1202416561
040 ## - CATALOGING SOURCE
Original cataloging agency DG1
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency DG1
Modifying agency OCLCO
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA331
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515/.222
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Preferred name for the person Simon, Jacques,
Authority record control number http://id.loc.gov/authorities/names/no2007077202
Relator term author.
245 10 - TITLE STATEMENT
Title Continuous functions /
Statement of responsibility, etc Jacques Simon.
264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc London, UK :
Name of publisher, distributor, etc ISTE, Ltd. ;
Place of publication, distribution, etc Hoboken :
Name of publisher, distributor, etc Wiley,
Date of publication, distribution, etc 2020.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent.
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia.
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier.
340 ## - PHYSICAL MEDIUM
Source rdacc
Authority record control number or standard number http://rdaregistry.info/termList/RDAColourContent/1003.
490 1# - SERIES STATEMENT
Series statement Analysis for PDEs set ;
Volume number/sequential designation volume 2.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
505 0# - CONTENTS
Formatted contents note Table of Contents<br/>Introduction ix<br/><br/>Familiarization with Semi-normed Spaces xiii<br/><br/>Notations xv<br/><br/>Chapter 1. Spaces of Continuous Functions 1<br/><br/>1.1. Notions of continuity 1<br/><br/>1.2. Spaces C(Ω;E), Cb(Ω;E), CK(Ω;E), C(Ω;E) and Cb(Ω;E) 3<br/><br/>1.3. Comparison of spaces of continuous functions 6<br/><br/>1.4. Sequential completeness of spaces of continuous functions 10<br/><br/>1.5. Metrizability of spaces of continuous functions 11<br/><br/>1.6. The space K(Ω;E) 14<br/><br/>1.7. Continuous mappings 20<br/><br/>1.8. Continuous extension and restriction 22<br/><br/>1.9. Separation and permutation of variables 23<br/><br/>1.10. Sequential compactness in Cb(Ω;E) 28<br/><br/>Chapter 2. Differentiable Functions 31<br/><br/>2.1. Differentiability 31<br/><br/>2.2. Finite increment theorem 34<br/><br/>2.3. Partial derivatives 37<br/><br/>2.4. Higher order partial derivatives 40<br/><br/>2.5. Spaces Cm(Ω;E), Cmb (Ω;E), CmK(Ω;E), Cmb (Ω;E) and Km(Ω;E) 42<br/><br/>2.6. Comparison and metrizability of spaces of differentiable functions 45<br/><br/>2.7. Filtering properties of spaces of differentiable functions 47<br/><br/>2.8. Sequential completeness of spaces of differentiable functions 49<br/><br/>2.9. The space Cm(Ω;E) and the set Cm(Ω;U) 52<br/><br/>Chapter 3. Differentiating Composite Functions and Others 55<br/><br/>3.1. Image under a linear mapping 55<br/><br/>3.2. Image under a multilinear mapping: Leibniz rule 59<br/><br/>3.3. Dual formula of the Leibniz rule 63<br/><br/>3.4. Continuity of the image under a multilinear mapping 65<br/><br/>3.5. Change of variables in a derivative 69<br/><br/>3.6. Differentiation with respect to a separated variable 72<br/><br/>3.7. Image under a differentiable mapping 73<br/><br/>3.8. Differentiation and translation 77<br/><br/>3.9. Localizing functions 79<br/><br/>Chapter 4. Integrating Uniformly Continuous Functions 83<br/><br/>4.1. Measure of an open subset of ℝd 83<br/><br/>4.2. Integral of a uniformly continuous function 87<br/><br/>4.3. Case where E is not a Neumann space 92<br/><br/>4.4. Properties of the integral 93<br/><br/>4.5. Dependence of the integral on the domain of integration 96<br/><br/>4.6. Additivity with respect to the domain of integration 99<br/><br/>4.7. Continuity of the integral 101<br/><br/>4.8. Differentiating under the integral sign 103<br/><br/>Chapter 5. Properties of the Measure of an Open Set 105<br/><br/>5.1. Additivity of the measure 105<br/><br/>5.2. Negligible sets 107<br/><br/>5.3. Determinant of d vectors 112<br/><br/>5.4. Measure of a parallelepiped 115<br/><br/>Chapter 6. Additional Properties of the Integral 119<br/><br/>6.1. Contribution of a negligible set to the integral 119<br/><br/>6.2. Integration and differentiation in one dimension 120<br/><br/>6.3. Integration of a function of functions 123<br/><br/>6.4. Integrating a function of multiple variables 125<br/><br/>6.5. Integration between graphs 130<br/><br/>6.6. Integration by parts and weak vanishing condition for a function 133<br/><br/>6.7. Change of variables in an integral 135<br/><br/>6.8. Some particular changes of variables in an integral 142<br/><br/>Chapter 7. Weighting and Regularization of Functions 147<br/><br/>7.1. Weighting 147<br/><br/>7.2. Properties of weighting 150<br/><br/>7.3. Weighting of differentiable functions 153<br/><br/>7.4. Local regularization 157<br/><br/>7.5. Global regularization 162<br/><br/>7.6. Partition of unity 166<br/><br/>7.7. Separability of K∞(Ω) 170<br/><br/>Chapter 8. Line Integral of a Vector Field Along a Path 173<br/><br/>8.1. Paths 173<br/><br/>8.2. Line integral of a field along a path 176<br/><br/>8.3. Line integral along a concatenation of paths 181<br/><br/>8.4. Tubular flow and the concentration theorem 183<br/><br/>8.5. Invariance under homotopy of the line integral of a local gradient 186<br/><br/>Chapter 9. Primitives of Continuous Functions 191<br/><br/>9.1. Explicit primitive of a field with line integral zero 191<br/><br/>9.2. Primitive of a field orthogonal to the divergence-free test fields 194<br/><br/>9.3. Gluing of local primitives on a simply connected open set 195<br/><br/>9.4. Explicit primitive on a star-shaped set: Poincaré’s theorem 197<br/><br/>9.5. Explicit primitive under the weak Poincaré condition 199<br/><br/>9.6. Primitives on a simply connected open set 203<br/><br/>9.7. Comparison of the existence conditions for a primitive 205<br/><br/>9.8. Fields with local primitives but no global primitive 208<br/><br/>9.9. Uniqueness of primitives 210<br/><br/>9.10. Continuous primitive mapping 211<br/><br/>Chapter 10. Additional Results: Integration on a Sphere 213<br/><br/>10.1. Surface integration on a sphere 213<br/><br/>10.2. Properties of the integral on a sphere 215<br/><br/>10.3. Radial calculation of integrals 218<br/><br/>10.4. Surface integral as an integral of dimension d − 1 220<br/><br/>10.5. A Stokes formula 224<br/><br/>Appendix 227<br/><br/>Bibliography 239<br/><br/>Index 243
520 ## - SUMMARY, ETC.
Summary, etc This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.
545 0# - BIOGRAPHICAL OR HISTORICAL DATA
Biographical or historical note Jacques Simon is Honorary Research Director at CNRS. His research focuses on Navier-Stokes equations, particularly in shape optimization and in the functional spaces they use.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Functions, Continuous.
Authority record control number http://id.loc.gov/authorities/subjects/sh85052334.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Analysis for PDEs set ;
Authority record control number http://id.loc.gov/authorities/names/no2018019311
Volume number/sequential designation v. 2.
856 ## - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier https://onlinelibrary.wiley.com/doi/book/10.1002/9781119332244
Link text Full text is available at Wiley Online Library Click here to view
942 ## - ADDED ENTRY ELEMENTS
Source of classification or shelving scheme
Item type EBOOK
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Permanent Location Current Location Date acquired Source of acquisition Inventory number Full call number Barcode Date last seen Price effective from Item type
          COLLEGE LIBRARY COLLEGE LIBRARY 2024-12-12 Megatexts Phil. Inc. 52304 515.222 Si541 2020 CL-52304 2024-12-12 2024-12-12 EBOOK