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.
Inhaltsverzeichnis
About the Author xv
Preface xvii
Introduction 1
1 Toy Model I-1: {−Δ, 0, Δ} 19
2 Toy Model I-2:{0, Δ, 2Δ} 31
3 Toy Model I-3: {−2Δ, −Δ, 0} 39
4 Toy Model I-4: {−Δ, 0, Δ} 47
5 Toy Model I-5: {−2Δ, −Δ, 0, Δ, 2Δ} 59
6 Toy Model I-7: {−3Δ, −2Δ, −Δ, 0, Δ, 2Δ, 3Δ} 79
7 Self-consistent Expressions for |D (n) > 111
8 Toy Model I-3: {Δ −1 , Δ 0 , Δ 1 } 125
9 Toy Model I-5: {Δ −2 , Δ −1 , Δ 0 , Δ 1 , Δ 2 } 165
10 Toy Model I-6: {Δ −3 , Δ −2 , Δ −1 , Δ 0 , Δ 1 , Δ 2 , Δ 3 } 207
11 Toy Model I-7: {Δ −3 , Δ −2 , Δ −1 , Δ 0 , Δ 1 , Δ 2 , Δ 3 } 231
12 Toy Model II: {{−Δ 1 , 0, Δ 1 }, {−Δ 2 , 0, Δ 2 }} 283
13 Toy Model III: {−Δ 1 , Δ 1 }×{−Δ 2 , Δ 2 }×{−Δ 3 , Δ 3 } 317
14 Solidification and Further Refinements 527
Appendix A The Canonical Matrix C 3×3 and Its Inverse 609
Appendix B The Canonical Matrix C 3×3 and Its Inverse Revisited 615
Appendix C The Canonical Matrix C 4×4 and Its Inverse 621
Appendix D The Canonical Matrix C 5×5 635
Appendix E The Canonical Matrix C 7×7 643
Index 657
Über den Autor
Alireza Baghai-Wadji, Ph D, 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.
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