Integral and discrete transforms with applications and error analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Dekker
1992
|
| Series: | Pure and applied mathematics
162 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 825 S. graph. Darst. |
| ISBN: | 0824782526 |
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MARC
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| 245 | 1 | 0 | |a Integral and discrete transforms with applications and error analysis |c Abdul J. Jerri |
| 264 | 1 | |a New York u.a. |b Dekker |c 1992 | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface v
Guide to Course Adoption ix
Chapter 1 Compatible Transforms 1
1.1 The Method of Separation of Variables and the Integral
Transforms 2
1.1.1 Integral Transforms 6
1.2 Compatible Transforms 7
1.2.1 Examples of Compatible Transforms 10
1.2.2 Nonlinear Terms 20
1.3 Classification of the Transforms 20
1.3.1 Integral Transforms 21
1.3.2 Band Limited Functions (or Transforms) 21
1.3.3 Finite Transforms—the Fourier Coefficients 23
1.3.4 The Truncation and Discretization (Sampling) Errors 26
1.3.5 The Discrete Transforms 27
1.4 Comments on the Inverse Transforms—Tables of the
Transforms 29
1.4.1 Integral Equations—Basic Definitions 30
1.5 The Compatible Transform and the Adjoint Problem 30
1.5.1 The Adjoint Differential Operator 32
1.5.2 The Two Eigenvalue Problems 36
xl
Xll CONTENTS
1.6 Constructing the Compatible Transforms for Self Adjoint
Problems—Second Order Differential Equations 49
1.6.1 Examples of the Sturm Liouville and Other
Transforms—Boundary Value Problems 52
1.6.2 A Remark Concerning Initial Value Problems 56
1.7 The nth Order Differential Operator 58
Relevant References to Chapter 1 63
Exercises 63
Chapter 2 Integral Transforms 81
2.1 Laplace Transforms 82
2.1.1 Transform Pairs and Operations 91
2.1.2 The Convolution Theorem for Laplace Transforms 104
2.1.3 Solution of Initial Value Problems Associated with
Ordinary and Partial Differential Equations 111
2.1.4 Applications to Volterra Integral Equations with
Difference Kernels 121
2.1.5 The z Transform 127
2.2 Fourier Exponential Transforms 128
2.2.1 Existence of the Fourier Transform and Its
Inverse—the Fourier Integral Formula 132
2.2.2 Basic Properties and the Convolution Theorem 157
2.3 Boundary and Initial Value Problems—Solutions by Fourier
Transforms 171
2.3.1 The Heat Equation on an Infinite Domain 171
2.3.2 The Wave Equation 174
2.3.3 The Schrodinger Equation 176
2.3.4 The Laplace Equation 181
2.4 Signals and Linear Systems—Representation in the Fourier
(Spectrum) Space 183
2.4.1 Linear Systems 184
2.4.2 Bandlimited Functions—the Sampling Expansion 204
2.4.3 Bandlimited Functions and B Splines (Hill Functions) 212
2.5 Fourier Sine and Cosine Transforms 213
2.5.1 Compatibility of the Fourier Sine and Cosine
Transforms with Even Order Derivatives 216
2.5.2 Applications to Boundary Value Problems on
Semi Infinite Domain 219
2.6 Higher Dimensional Fourier Transforms 224
2.6.1 Relation Between the Hankel Transform and the
Multiple Fourier Transform—Circular Symmetry 231
CONTENTS Xlll
2.6.2 The Double Fourier Transform of Functions with
Circular Symmetry—The /O Hankel Transform 233
2.6.3 A Double Fourier Transform Convolution Theorem
for the /o Hankel Transform 236
2.7 The Hankel (Bessel) Transforms 236
2.7.1 Applications of the Hankel Transforms 242
2.8 Laplace Transform Inversion 251
2.8.1 Fourier Transform in the Complex Plane 251
2.8.2 The Laplace Transform Inversion Formula 253
2.8.3 The Numerical Inversion of the Laplace Transform 254
2.8.4 Applications 255
2.9 Other Important Integral Transforms 257
2.9.1 Hilbert Transform 257
2.9.2 Mellin Transform 257
2.9.3 The z Transform and the Laplace Transform 258
Relevant References for Chapter 2 261
Exercises 261
Chapter 3 Finite Transforms—Fourier Series and Coefficients 329
3.1 Fourier (Trigonometric) Series and General Orthogonal
Expansion 332
3.1.1 Convergence of the Fourier Series 343
3.1.2 Elements of Infinite Series—Convergence Theorems 372
3.1.3 The Orthogonal Expansions—Bessel s Inequality and
Fourier Series 384
3.2 Fourier Sine and Cosine Transforms 421
3.3 Fourier (Exponential) Transforms 427
3.3.1 The Finite Fourier Exponential Transform and the
Sampling Expansion 429
3.4 Hankel (Bessel) Transforms 433
3.4.1 Another Finite Hankel Transform 437
3.5 Classical Orthogonal Polynomial Transforms 440
3.5.1 Legendre Transforms 441
3.5.2 Laguerre Transform 445
3.5.3 Hermite Transforms 446
3.5.4 Tchebychev Transforms 447
3.6 The Generalized Sampling Expansion 449
3.6.1 Generalized Translation and Convolution Products 452
3.6.2 Impulse Train for Bessel Orthogonal Series Expansion
for a (New) Bessel Type Poisson Summation Formula 456
XlV CONTENTS
3.7 A Remark on the Transform Methods and Nonlinear
Problems 461
Relevant References to Chapter 3 464
Exercises 465
Chapter 4 Discrete Transforms 509
4.1 Discrete Fourier Transforms 510
4.1.1 Fourier Integrals, Series, and the Discrete Transforms 514
4.1.2 Computing for Complex Valued Functions 532
4.1.3 The Fast Fourier Transform 547
4.1.4 Construction and Basic Properties of the Discrete
Transforms 553
4.1.5 Operational Difference Calculus for the DFT and
the z Transform 573
4.1.6 Approximating Fourier Integrals and Series by
Discrete Fourier Transforms 593
4.1.7 Examples of Computing Fourier Integrals and Series 637
4.2 Discrete Orthogonal Polynomial Transforms 645
4.2.1 Basic Properties and Illustrations 646
4.2.2 Properties of the Discrete Legendre Transforms 649
4.2.3 The Use of the Discrete Orthogonal Polynomial
Transforms 651
4.3 Bessel type Poisson Summation Formula (for the
Bessel Fourier Series and Hankel Transforms) 656
Relevant References for Chapter 4 662
Exercises 663
Appendix A Basic Second Order Differential Equations and
Their (Series) Solutions—Special Functions 689
A.1 Introduction 689
A.2 Method of Variation of Parameters 691
A.3 Power Series Method of Solution 694
A.4 Frobenius Method of Solution—Power Series Expansion
About a Regular Singular Point 699
A.5 Special Differential Equations and Their Solutions 702
A.5.1 Bessel s Equation 703
A.5.2 Legendre s Equation 705
A.5.3 Other Special Equations 710
Exercises 713
CONTENTS XV
Appendix B Mathematical Modeling of Partial Differential
Equations—Boundary and Initial Value Problems 741
B.I Partial Differential Equations for Vibrating Systems 742
B.2 Diffusion (or Heat Conduction) Equation 748
Exercises 752
Appendix C Tables of Transforms 765
C.I Laplace Transforms 766
C.2 Fourier Exponential Transforms 769
C.3 Fourier Sine Transforms 773
C.4 Fourier Cosine Transforms 777
C.5 Hankel Transforms 780
C.6 Mellin Transforms 782
C.7 Hilbert Transforms 783
C.8 Finite Exponential Transforms 784
C.9 Finite Sine Transforms 785
CIO Finite Cosine Transforms 788
C.ll Finite (First) Hankel Transforms, Jn( ka) = 0 792
C.12 Finite (Second) Hankel Transforms,
XkJ^Xka) + hJn(Xka) = 0 793
C.13 Finite Legendre Transforms 794
C.14 Finite Tchebychev Transforms 796
C.I5 Finite Laguerre Transforms 796
C.16 Finite Hermite Transforms 796
C.17 z Transforms 797
Bibliography 799
Index of Notations 809
Subject Index 813
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T16:29:48Z |
| institution | BVB |
| isbn | 0824782526 |
| language | English |
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| spelling | Jerri, Abdul J. Verfasser aut Integral and discrete transforms with applications and error analysis Abdul J. Jerri New York u.a. Dekker 1992 XV, 825 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 162 Diskrete Fourier-Transformation Fourier-Transformation Schnelle Fourier-Transformation Randwertproblem (DE-588)4048395-2 gnd rswk-swf Integraltransformation (DE-588)4027235-7 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf Diskrete Fourier-Transformation (DE-588)4150175-5 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s DE-604 Diskrete Fourier-Transformation (DE-588)4150175-5 s Transformation Mathematik (DE-588)4060637-5 s Anfangswertproblem (DE-588)4001991-3 s DE-188 Randwertproblem (DE-588)4048395-2 s Pure and applied mathematics 162 (DE-604)BV000001885 162 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412501&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jerri, Abdul J. Integral and discrete transforms with applications and error analysis Pure and applied mathematics Diskrete Fourier-Transformation Fourier-Transformation Schnelle Fourier-Transformation Randwertproblem (DE-588)4048395-2 gnd Integraltransformation (DE-588)4027235-7 gnd Anfangswertproblem (DE-588)4001991-3 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4027235-7 (DE-588)4001991-3 (DE-588)4150175-5 (DE-588)4060637-5 |
| title | Integral and discrete transforms with applications and error analysis |
| title_auth | Integral and discrete transforms with applications and error analysis |
| title_exact_search | Integral and discrete transforms with applications and error analysis |
| title_full | Integral and discrete transforms with applications and error analysis Abdul J. Jerri |
| title_fullStr | Integral and discrete transforms with applications and error analysis Abdul J. Jerri |
| title_full_unstemmed | Integral and discrete transforms with applications and error analysis Abdul J. Jerri |
| title_short | Integral and discrete transforms with applications and error analysis |
| title_sort | integral and discrete transforms with applications and error analysis |
| topic | Diskrete Fourier-Transformation Fourier-Transformation Schnelle Fourier-Transformation Randwertproblem (DE-588)4048395-2 gnd Integraltransformation (DE-588)4027235-7 gnd Anfangswertproblem (DE-588)4001991-3 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| topic_facet | Diskrete Fourier-Transformation Fourier-Transformation Schnelle Fourier-Transformation Randwertproblem Integraltransformation Anfangswertproblem Transformation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412501&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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