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The Resource Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
Resource Information
The item Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximationtheoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or selfstudy reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas
 Language

 eng
 eng
 Edition
 1st ed. 2005.
 Extent
 1 online resource (165 p.)
 Note
 Description based upon print version of record
 Contents

 1 Approximation with Polynomials
 1.1 Approximation of a function on an interval
 1.2 Weierstrass’ theorem
 1.3 Taylor’s theorem
 1.4 Exercises
 2 Infinite Series
 2.1 Infinite series of numbers
 2.2 Estimating the sum of an infinite series
 2.3 Geometric series
 2.4 Power series
 2.5 General infinite sums of functions
 2.6 Uniform convergence
 2.7 Signal transmission
 2.8 Exercises
 3 Fourier Analysis
 3.1 Fourier series
 3.2 Fourier’s theorem and approximation
 3.3 Fourier series and signal analysis
 3.4 Fourier series and Hilbert spaces
 3.5 Fourier series in complex form
 3.6 Parseval’s theorem
 3.7 Regularity and decay of the Fourier coefficients
 3.8 Best Nterm approximation
 3.9 The Fourier transform
 3.10 Exercises
 4 Wavelets and Applications
 4.1 About wavelet systems
 4.2 Wavelets and signal processing
 4.3 Wavelets and fingerprints
 4.4 Wavelet packets
 4.5 Alternatives to wavelets: Gabor systems
 4.6 Exercises
 5 Wavelets and their Mathematical Properties
 5.1 Wavelets and L2 (?)
 5.2 Multiresolution analysis
 5.3 The role of the Fourier transform
 5.4 The Haar wavelet
 5.5 The role of compact support
 5.6 Wavelets and singularities
 5.7 Best Nterm approximation
 5.8 Frames
 5.9 Gabor systems
 5.10 Exercises
 Appendix A
 A.1 Definitions and notation
 A.2 Proof of Weierstrass’ theorem
 A.3 Proof of Taylor’s theorem
 A.4 Infinite series
 A.5 Proof of Theorem 3 7 2
 Appendix B
 B.1 Power series
 B.2 Fourier series for 2?periodic functions
 List of Symbols
 References
 Isbn
 9780817644482
 Label
 Approximation Theory : From Taylor Polynomials to Wavelets
 Title
 Approximation Theory
 Title remainder
 From Taylor Polynomials to Wavelets
 Statement of responsibility
 by Ole Christensen, Khadija Laghrida Christensen
 Language

 eng
 eng
 Summary
 This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximationtheoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or selfstudy reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas
 http://library.link/vocab/creatorName
 Christensen, Ole
 Dewey number
 511/.4
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 Huz9oyahSA0
 UY7d3rUZkFU
 Language note
 English
 LC call number
 QA403.5404.5
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Christensen, Khadija Laghrida.
 Series statement

 Applied and numerical harmonic analysis
 Applied and Numerical Harmonic Analysis,
 http://library.link/vocab/subjectName

 Fourier analysis
 Mathematics
 Harmonic analysis
 Functional analysis
 Fourier Analysis
 Approximations and Expansions
 Abstract Harmonic Analysis
 Functional Analysis
 Applications of Mathematics
 Signal, Image and Speech Processing
 Label
 Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [153]154) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 1 Approximation with Polynomials  1.1 Approximation of a function on an interval  1.2 Weierstrass’ theorem  1.3 Taylor’s theorem  1.4 Exercises  2 Infinite Series  2.1 Infinite series of numbers  2.2 Estimating the sum of an infinite series  2.3 Geometric series  2.4 Power series  2.5 General infinite sums of functions  2.6 Uniform convergence  2.7 Signal transmission  2.8 Exercises  3 Fourier Analysis  3.1 Fourier series  3.2 Fourier’s theorem and approximation  3.3 Fourier series and signal analysis  3.4 Fourier series and Hilbert spaces  3.5 Fourier series in complex form  3.6 Parseval’s theorem  3.7 Regularity and decay of the Fourier coefficients  3.8 Best Nterm approximation  3.9 The Fourier transform  3.10 Exercises  4 Wavelets and Applications  4.1 About wavelet systems  4.2 Wavelets and signal processing  4.3 Wavelets and fingerprints  4.4 Wavelet packets  4.5 Alternatives to wavelets: Gabor systems  4.6 Exercises  5 Wavelets and their Mathematical Properties  5.1 Wavelets and L2 (?)  5.2 Multiresolution analysis  5.3 The role of the Fourier transform  5.4 The Haar wavelet  5.5 The role of compact support  5.6 Wavelets and singularities  5.7 Best Nterm approximation  5.8 Frames  5.9 Gabor systems  5.10 Exercises  Appendix A  A.1 Definitions and notation  A.2 Proof of Weierstrass’ theorem  A.3 Proof of Taylor’s theorem  A.4 Infinite series  A.5 Proof of Theorem 3 7 2  Appendix B  B.1 Power series  B.2 Fourier series for 2?periodic functions  List of Symbols  References
 Dimensions
 unknown
 Edition
 1st ed. 2005.
 Extent
 1 online resource (165 p.)
 Form of item
 online
 Isbn
 9780817644482
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780817644482
 Specific material designation
 remote
 System control number

 (CKB)2670000000276765
 (EBL)3068768
 (SSID)ssj0000755051
 (PQKBManifestationID)11399439
 (PQKBTitleCode)TC0000755051
 (PQKBWorkID)10729495
 (PQKB)11789492
 (DEHe213)9780817644482
 (MiAaPQ)EBC3068768
 (EXLCZ)992670000000276765
 Label
 Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [153]154) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 1 Approximation with Polynomials  1.1 Approximation of a function on an interval  1.2 Weierstrass’ theorem  1.3 Taylor’s theorem  1.4 Exercises  2 Infinite Series  2.1 Infinite series of numbers  2.2 Estimating the sum of an infinite series  2.3 Geometric series  2.4 Power series  2.5 General infinite sums of functions  2.6 Uniform convergence  2.7 Signal transmission  2.8 Exercises  3 Fourier Analysis  3.1 Fourier series  3.2 Fourier’s theorem and approximation  3.3 Fourier series and signal analysis  3.4 Fourier series and Hilbert spaces  3.5 Fourier series in complex form  3.6 Parseval’s theorem  3.7 Regularity and decay of the Fourier coefficients  3.8 Best Nterm approximation  3.9 The Fourier transform  3.10 Exercises  4 Wavelets and Applications  4.1 About wavelet systems  4.2 Wavelets and signal processing  4.3 Wavelets and fingerprints  4.4 Wavelet packets  4.5 Alternatives to wavelets: Gabor systems  4.6 Exercises  5 Wavelets and their Mathematical Properties  5.1 Wavelets and L2 (?)  5.2 Multiresolution analysis  5.3 The role of the Fourier transform  5.4 The Haar wavelet  5.5 The role of compact support  5.6 Wavelets and singularities  5.7 Best Nterm approximation  5.8 Frames  5.9 Gabor systems  5.10 Exercises  Appendix A  A.1 Definitions and notation  A.2 Proof of Weierstrass’ theorem  A.3 Proof of Taylor’s theorem  A.4 Infinite series  A.5 Proof of Theorem 3 7 2  Appendix B  B.1 Power series  B.2 Fourier series for 2?periodic functions  List of Symbols  References
 Dimensions
 unknown
 Edition
 1st ed. 2005.
 Extent
 1 online resource (165 p.)
 Form of item
 online
 Isbn
 9780817644482
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780817644482
 Specific material designation
 remote
 System control number

 (CKB)2670000000276765
 (EBL)3068768
 (SSID)ssj0000755051
 (PQKBManifestationID)11399439
 (PQKBTitleCode)TC0000755051
 (PQKBWorkID)10729495
 (PQKB)11789492
 (DEHe213)9780817644482
 (MiAaPQ)EBC3068768
 (EXLCZ)992670000000276765
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/ApproximationTheoryFromTaylorPolynomialsto/rcr0Ubl1iY4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/ApproximationTheoryFromTaylorPolynomialsto/rcr0Ubl1iY4/">Approximation Theory : From Taylor Polynomials to Wavelets, by Ole Christensen, Khadija Laghrida Christensen, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>