
Discrete Taylor Transform and Inverse Transform
Alireza Baghai-Wadji(Author)
Wiley-IEEE Press
1st Edition
Published on 29. November 2024
Book
Hardback
688 pages
978-1-394-24007-4 (ISBN)
Description
Revolutionize the calculation of mixed derivatives with this groundbreaking text
Transform and inverse transform techniques, such as the Fourier transform and the Laplace transform, enable scientists and engineers to conduct research and design in transformed domains where the work is simpler, after which the results can be converted back into the real domain where they can be applied or actualized. This latter stage in the process, the inverse transform, ordinarily poses significant challenges. New transform/inverse transform techniques carry extraordinary potential to produce revolutionary new science and engineering solutions.
Discrete Taylor Transform and Inverse Transform presents the groundbreaking discovery of a new transform technique. Placing a novel emphasis on the "position variable" and "derivative operator" as main actors, the Discrete Taylor Transform and Inverse Transform (D-TTIT) will facilitate the calculation of mixed derivatives of multivariate functions to any desired order. The result promises to create new applications not only in its allied fields of quantum physics and quantum engineering, but potentially much more widely.
Readers will also find:
Discussion of possible applications in electrical engineering, acoustics, photonics, and many more
Analysis of functions depending on one, two, or three independent variables
Tools for theoreticians and practitioners to design their own algorithms for solving specific boundary-value problems
Discrete Taylor Transform and Inverse Transform is ideal for any scientific or engineering professional looking to understand a cutting-edge research and design tool.
Transform and inverse transform techniques, such as the Fourier transform and the Laplace transform, enable scientists and engineers to conduct research and design in transformed domains where the work is simpler, after which the results can be converted back into the real domain where they can be applied or actualized. This latter stage in the process, the inverse transform, ordinarily poses significant challenges. New transform/inverse transform techniques carry extraordinary potential to produce revolutionary new science and engineering solutions.
Discrete Taylor Transform and Inverse Transform presents the groundbreaking discovery of a new transform technique. Placing a novel emphasis on the "position variable" and "derivative operator" as main actors, the Discrete Taylor Transform and Inverse Transform (D-TTIT) will facilitate the calculation of mixed derivatives of multivariate functions to any desired order. The result promises to create new applications not only in its allied fields of quantum physics and quantum engineering, but potentially much more widely.
Readers will also find:
Discussion of possible applications in electrical engineering, acoustics, photonics, and many more
Analysis of functions depending on one, two, or three independent variables
Tools for theoreticians and practitioners to design their own algorithms for solving specific boundary-value problems
Discrete Taylor Transform and Inverse Transform is ideal for any scientific or engineering professional looking to understand a cutting-edge research and design tool.
More details
Language
English
Place of publication
United States
Publishing group
John Wiley & Sons Inc
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 37 mm
Weight
1393 gr
ISBN-13
978-1-394-24007-4 (9781394240074)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Additional editions

Alireza Baghai-Wadji
Discrete Taylor Transform and Inverse Transform
E-Book
12/2024
1st Edition
Wiley
€133.99
Available for download

Alireza Baghai-Wadji
Discrete Taylor Transform and Inverse Transform
E-Book
12/2024
1st Edition
Wiley
€133.99
Available for download
Person
Alireza Baghai-Wadji, PhD, DSc, is Professor Emeritus of Electronics and Computational Engineering at the University of Cape Town, South Africa. His contributions to mathematical physics include automatic diagonalization of PDEs in physics, construction of physics-inspired Dirac delta functions, and the development of algebraic and exponential regularization techniques for taming infinities and zooming into the nearfields.
Content
About the Author xv
Preface xvii
Introduction 1
1 Toy Model I-1: {??, 0, ?} 19
2 Toy Model I-2:{0, ?, 2?} 31
3 Toy Model I-3: {?2?, ??, 0} 39
4 Toy Model I-4: {??, 0, ?} 47
5 Toy Model I-5: {?2?, ??, 0, ?, 2?} 59
6 Toy Model I-7: {?3?, ?2?, ??, 0, ?, 2?, 3?} 79
7 Self-consistent Expressions for |D (n) > 111
8 Toy Model I-3: {? ?1 , ? 0 , ? 1 } 125
9 Toy Model I-5: {? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 } 165
10 Toy Model I-6: {? ?3 , ? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 , ? 3 } 207
11 Toy Model I-7: {? ?3 , ? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 , ? 3 } 231
12 Toy Model II: {<!-- -->{?? 1 , 0, ? 1 }, {?? 2 , 0, ? 2 }} 283
13 Toy Model III: {?? 1 , ? 1 }x{?? 2 , ? 2 }x{?? 3 , ? 3 } 317
14 Solidification and Further Refinements 527
Appendix A The Canonical Matrix C 3x3 and Its Inverse 609
Appendix B The Canonical Matrix C 3x3 and Its Inverse Revisited 615
Appendix C The Canonical Matrix C 4x4 and Its Inverse 621
Appendix D The Canonical Matrix C 5x5 635
Appendix E The Canonical Matrix C 7x7 643
Index 657
Preface xvii
Introduction 1
1 Toy Model I-1: {??, 0, ?} 19
2 Toy Model I-2:{0, ?, 2?} 31
3 Toy Model I-3: {?2?, ??, 0} 39
4 Toy Model I-4: {??, 0, ?} 47
5 Toy Model I-5: {?2?, ??, 0, ?, 2?} 59
6 Toy Model I-7: {?3?, ?2?, ??, 0, ?, 2?, 3?} 79
7 Self-consistent Expressions for |D (n) > 111
8 Toy Model I-3: {? ?1 , ? 0 , ? 1 } 125
9 Toy Model I-5: {? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 } 165
10 Toy Model I-6: {? ?3 , ? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 , ? 3 } 207
11 Toy Model I-7: {? ?3 , ? ?2 , ? ?1 , ? 0 , ? 1 , ? 2 , ? 3 } 231
12 Toy Model II: {<!-- -->{?? 1 , 0, ? 1 }, {?? 2 , 0, ? 2 }} 283
13 Toy Model III: {?? 1 , ? 1 }x{?? 2 , ? 2 }x{?? 3 , ? 3 } 317
14 Solidification and Further Refinements 527
Appendix A The Canonical Matrix C 3x3 and Its Inverse 609
Appendix B The Canonical Matrix C 3x3 and Its Inverse Revisited 615
Appendix C The Canonical Matrix C 4x4 and Its Inverse 621
Appendix D The Canonical Matrix C 5x5 635
Appendix E The Canonical Matrix C 7x7 643
Index 657