{"product_id":"discrete-taylor-transform-and-inverse-transform-isbn-9781394240074","title":"Discrete Taylor Transform and Inverse Transform","description":"\u003cp\u003e\u003cb\u003eRevolutionize the calculation of mixed derivatives with this groundbreaking text\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eTransform 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eDiscrete Taylor Transform and Inverse Transform\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eDiscussion of possible applications in electrical engineering, acoustics, photonics, and many more\u003c\/li\u003e\n\u003cli\u003e Analysis of functions depending on one, two, or three independent variables\u003c\/li\u003e\n\u003cli\u003e Tools for theoreticians and practitioners to design their own algorithms for solving specific boundary-value problems\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eDiscrete Taylor Transform and Inverse Transform\u003c\/i\u003e is ideal for any scientific or engineering professional looking to understand a cutting-edge research and design tool. \u003c\/p\u003e\u003cp\u003eAbout the Author xv\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e1 Toy Model I-1: {−Δ, 0, Δ} 19\u003c\/p\u003e \u003cp\u003e2 Toy Model I-2:{0, Δ, 2Δ} 31\u003c\/p\u003e \u003cp\u003e3 Toy Model I-3: {−2Δ, −Δ, 0} 39\u003c\/p\u003e \u003cp\u003e4 Toy Model I-4: {−Δ, 0, Δ} 47\u003c\/p\u003e \u003cp\u003e5 Toy Model I-5: {−2Δ, −Δ, 0, Δ, 2Δ} 59\u003c\/p\u003e \u003cp\u003e6 Toy Model I-7: {−3Δ, −2Δ, −Δ, 0, Δ, 2Δ, 3Δ} 79\u003c\/p\u003e \u003cp\u003e7 Self-consistent Expressions for |D \u003csup\u003e(n) \u003c\/sup\u003e\u0026gt; 111\u003c\/p\u003e \u003cp\u003e8 Toy Model I-3: {Δ \u003csub\u003e−1 \u003c\/sub\u003e, Δ \u003csub\u003e0\u003c\/sub\u003e , Δ \u003csub\u003e1\u003c\/sub\u003e } 125\u003c\/p\u003e \u003cp\u003e9 Toy Model I-5: {Δ \u003csub\u003e−2 \u003c\/sub\u003e, Δ \u003csub\u003e−1\u003c\/sub\u003e , Δ \u003csub\u003e0\u003c\/sub\u003e , Δ \u003csub\u003e1\u003c\/sub\u003e , Δ \u003csub\u003e2\u003c\/sub\u003e } 165\u003c\/p\u003e \u003cp\u003e10 Toy Model I-6: {Δ \u003csub\u003e−3\u003c\/sub\u003e , Δ \u003csub\u003e−2\u003c\/sub\u003e , Δ \u003csub\u003e−1\u003c\/sub\u003e , Δ \u003csub\u003e0\u003c\/sub\u003e , Δ \u003csub\u003e1\u003c\/sub\u003e , Δ \u003csub\u003e2\u003c\/sub\u003e , Δ \u003csub\u003e3\u003c\/sub\u003e } 207\u003c\/p\u003e \u003cp\u003e11 Toy Model I-7: {Δ \u003csub\u003e−3\u003c\/sub\u003e , Δ \u003csub\u003e−2\u003c\/sub\u003e , Δ \u003csub\u003e−1\u003c\/sub\u003e , Δ \u003csub\u003e0\u003c\/sub\u003e , Δ \u003csub\u003e1\u003c\/sub\u003e , Δ \u003csub\u003e2\u003c\/sub\u003e , Δ \u003csub\u003e3\u003c\/sub\u003e } 231\u003c\/p\u003e \u003cp\u003e12 Toy Model II: {{−Δ \u003csub\u003e1 \u003c\/sub\u003e, 0, Δ \u003csub\u003e1\u003c\/sub\u003e }, {−Δ \u003csub\u003e2\u003c\/sub\u003e , 0, Δ \u003csub\u003e2\u003c\/sub\u003e }} 283\u003c\/p\u003e \u003cp\u003e13 Toy Model III: {−Δ \u003csub\u003e1\u003c\/sub\u003e , Δ \u003csub\u003e1\u003c\/sub\u003e }×{−Δ \u003csub\u003e2\u003c\/sub\u003e , Δ \u003csub\u003e2\u003c\/sub\u003e }×{−Δ \u003csub\u003e3\u003c\/sub\u003e , Δ \u003csub\u003e3\u003c\/sub\u003e } 317\u003c\/p\u003e \u003cp\u003e14 Solidification and Further Refinements 527\u003c\/p\u003e \u003cp\u003eAppendix A The Canonical Matrix C \u003csub\u003e3×3\u003c\/sub\u003e and Its Inverse 609\u003c\/p\u003e \u003cp\u003eAppendix B The Canonical Matrix C \u003csub\u003e3×3\u003c\/sub\u003e and Its Inverse Revisited 615\u003c\/p\u003e \u003cp\u003eAppendix C The Canonical Matrix C \u003csub\u003e4×4\u003c\/sub\u003e and Its Inverse 621\u003c\/p\u003e \u003cp\u003eAppendix D The Canonical Matrix C \u003csub\u003e5×5\u003c\/sub\u003e 635\u003c\/p\u003e \u003cp\u003eAppendix E The Canonical Matrix C \u003csub\u003e7×7\u003c\/sub\u003e 643\u003c\/p\u003e \u003cp\u003eIndex 657\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eAlireza Baghai-Wadji, PhD, DSc,\u003c\/b\u003e 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.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eRevolutionize the calculation of mixed derivatives with this groundbreaking text\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eTransform 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eDiscrete Taylor Transform and Inverse Transform\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eDiscussion of possible applications in electrical engineering, acoustics, photonics, and many more\u003c\/li\u003e\n\u003cli\u003e Analysis of functions depending on one, two, or three independent variables\u003c\/li\u003e\n\u003cli\u003e Tools for theoreticians and practitioners to design their own algorithms for solving specific boundary-value problems\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eDiscrete Taylor Transform and Inverse Transform\u003c\/i\u003e is ideal for any scientific or engineering professional looking to understand a cutting-edge research and design tool.\u003c\/p\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Default Title","offer_id":47989074723045,"sku":"NP9781394240074","price":150.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781394240074.jpg?v=1761782689","url":"https:\/\/k12savings.com\/products\/discrete-taylor-transform-and-inverse-transform-isbn-9781394240074","provider":"K12savings","version":"1.0","type":"link"}