Mathematical theory of subdivision : (Record no. 93451)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 07154cam a2200613Ki 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9781315168265 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | FlBoTFG |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20260210180901.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu---unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190711s2019 flu ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | OCoLC-P |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | OCoLC-P |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781315168265 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 131516826X |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780429679247 |
| Qualifying information | (electronic bk. : Mobipocket) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0429679246 |
| Qualifying information | (electronic bk. : Mobipocket) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0429679416 |
| Qualifying information | (electronic bk. : EPUB) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781351685443 |
| Qualifying information | (electronic bk. : PDF) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1351685449 |
| Qualifying information | (electronic bk. : PDF) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780429679414 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781138051584 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 1138051586 |
| 024 8# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1201/9781315168265 |
| Source of number or code | doi |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1107880840 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC-P)1107880840 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QC20.7.F56 |
| Item number | K85 2019eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 000000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 003000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 021000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | UB |
| Source | bicssc |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 530.15/1825 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kumar, Sandeep |
| Titles and other words associated with a name | (Professor of mechanical engineering), |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Mathematical theory of subdivision : |
| Remainder of title | finite element and wavelet methods / |
| Statement of responsibility, etc | Sandeep Kumar, Ashish Pathak, Debasish Khan. |
| 264 #1 - | |
| -- | Boca Raton, Florida : |
| -- | CRC Press, |
| -- | [2019] |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. Presents a range of workout examples for better comprehension of spaces and operators. Algorithms are presented to facilitate computer programming. Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | <P>Preface</P><P>About the authors</P><OL><B><P></P></OL><P>1. Overview of finite element method</P><OL><P></P><OL></B><P><LI>Some common governing differential equations </LI><P></P><P><LI>Basic steps of finite element method </LI><P></P><P><LI>Element stiffness matrix for a bar </LI><P></P><P><LI>Element stiffness matrix for single variable 2d element </LI><P></P><P><LI>Element stiffness matrix for a beam element</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>2. Wavelets</P><OL><P></P></OL><OL><OL></B><P><LI>Wavelet basis functions</LI><P></P><P><LI>Wavelet-Galerkin method </LI><P></P><P><LI>Daubechies wavelets for boundary and initial value problems </LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>3. Fundamentals of vector spaces </P><OL><P></P></OL><OL><OL></B><P><LI>Introduction</LI><P></P><P><LI>Vector spaces </LI><P></P><P><LI>Normed linear spaces </LI><P></P><P><LI>Inner product spaces </LI><P></P><P><LI>Banach spaces </LI><P></P><P><LI>Hilbert spaces </LI><P></P><P><LI>Projection on finite dimensional spaces</LI><P></P><P><LI>Change of basis -- Gram-Schmidt othogonalization process</LI><P></P><P><LI>Riesz bases and frame conditions</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>4. Operators</P><OL><P></P></OL><OL><OL></B><P><LI>Mapping of sets, general concept of functions</LI><P></P><P><LI>Operators</LI><P></P><P><LI>Linear and adjoint operators</LI><P></P><P><LI>Functionals and dual space</LI><P></P><P><LI>Spectrum of bounded linear self-adjoint operator </LI><P></P><P><LI>Classification of differential operators</LI><P></P><P><LI>Existence, uniqueness and regularity of solution</LI><P></P><P><LI>References</LI><P></P></OL></OL><OL><B><P></P></OL><P>5. Theoretical foundations of the finite element method</B> </P><OL><P></P></OL><OL><OL><P><LI>Distribution theory</LI><P></P><P><LI>Sobolev spaces</LI><P></P><P><LI>Variational Method</LI><P></P><P><LI>Nonconforming elements and patch test</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>6. Wavelet- based methods for differential equations</P><OL><P></P></OL><OL><OL></B><P><LI>Fundamentals of continuous and discrete wavelets</LI><P></P><P><LI>Multiscaling</LI><P></P><P><LI>Classification of wavelet basis functions </LI><P></P><P><LI>Discrete wavelet transform </LI><P></P><P><LI>Lifting scheme for discrete wavelet transform </LI><P></P><P><LI>Lifting scheme to customize wavelets </LI><P></P><P><LI>Non-standard form of matrix and its solution </LI><P></P><P><LI>Multigrid method</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>7. Error -- estimation</B></P><OL><P></P><OL><P><LI>Introduction</LI><P></P><I><P><LI>A-priori</I> error estimation</LI><P></P><P><LI>Recovery based error estimators </LI><P></P><P><LI>Residual based error estimators </LI><P></P><P><LI>Goal oriented error estimators</LI><P></P><P><LI>Hierarchical & wavelet based error estimator</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><B><P>Appendix</B><I><I></P></I></I> |
| 588 ## - | |
| -- | OCLC-licensed vendor bibliographic record. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Finite element method. |
| 9 (RLIN) | 743 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Wavelets (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numerical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Harmonic analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Generalized spaces. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS / General |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS / Applied |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS / Number Systems |
| Source of heading or term | bisacsh |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Pathak, Ashish, |
| Relator term | author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Khan, Debasish, |
| Relator term | author. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Taylor & Francis |
| Uniform Resource Identifier | <a href="https://www.taylorfrancis.com/books/9781315168265">https://www.taylorfrancis.com/books/9781315168265</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | OCLC metadata license agreement |
| Uniform Resource Identifier | <a href="http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf">http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf</a> |
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