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Mathematical theory of subdivision : (Record no. 130902)

000 -LEADER
fixed length control field 07120cam a2200601Ki 4500
001 - CONTROL NUMBER
control field 9781315168265
003 - CONTROL NUMBER IDENTIFIER
control field FlBoTFG
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220509193140.0
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
-- (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 131516826X
-- (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780429679247
-- (electronic bk. : Mobipocket)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0429679246
-- (electronic bk. : Mobipocket)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0429679416
-- (electronic bk. : EPUB)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781351685443
-- (electronic bk. : PDF)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 1351685449
-- (electronic bk. : PDF)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780429679414
-- (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

Preface

About the authors

1. Overview of finite element method

    1. Some common governing differential equations

    2. Basic steps of finite element method

    3. Element stiffness matrix for a bar

    4. Element stiffness matrix for single variable 2d element

    5. Element stiffness matrix for a beam element

    6. References for further reading

2. Wavelets

    1. Wavelet basis functions

    2. Wavelet-Galerkin method

    3. Daubechies wavelets for boundary and initial value problems

    4. References for further reading

3. Fundamentals of vector spaces

    1. Introduction

    2. Vector spaces

    3. Normed linear spaces

    4. Inner product spaces

    5. Banach spaces

    6. Hilbert spaces

    7. Projection on finite dimensional spaces

    8. Change of basis -- Gram-Schmidt othogonalization process

    9. Riesz bases and frame conditions

    10. References for further reading

4. Operators

    1. Mapping of sets, general concept of functions

    2. Operators

    3. Linear and adjoint operators

    4. Functionals and dual space

    5. Spectrum of bounded linear self-adjoint operator

    6. Classification of differential operators

    7. Existence, uniqueness and regularity of solution

    8. References

5. Theoretical foundations of the finite element method

    1. Distribution theory

    2. Sobolev spaces

    3. Variational Method

    4. Nonconforming elements and patch test

    5. References for further reading

6. Wavelet- based methods for differential equations

    1. Fundamentals of continuous and discrete wavelets

    2. Multiscaling

    3. Classification of wavelet basis functions

    4. Discrete wavelet transform

    5. Lifting scheme for discrete wavelet transform

    6. Lifting scheme to customize wavelets

    7. Non-standard form of matrix and its solution

    8. Multigrid method

    9. References for further reading

7. Error -- estimation

    1. Introduction

    2. A-priori error estimation

    3. Recovery based error estimators

    4. Residual based error estimators

    5. Goal oriented error estimators

    6. Hierarchical & wavelet based error estimator

    7. References for further reading

Appendix
588 ## -
-- OCLC-licensed vendor bibliographic record.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Finite element method.
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 https://www.taylorfrancis.com/books/9781315168265
856 42 - ELECTRONIC LOCATION AND ACCESS
Materials specified OCLC metadata license agreement
Uniform Resource Identifier http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf

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