Zayed, Ahmed I.
Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems.The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included.The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:
PreliminariesSpecial FunctionsGeneralized FunctionsFunction TransformationsThe Laplace TransformThe Two-Sided Laplace TransformThe Borel TransformThe Stieltjes TransformThe Lambert TransformThe Mellin TransformThe Mellin-Type TransformThe Fourier TransformThe Hartley TransformThe Hilbert TransformThe Boas TransformThe Mittag-Leffler TransformThe Convolution TransformThe Weierstrass TransformThe Abel TransformThe Riemann-Liouville and Weyl Fractional IntegralsThe Hankel and Hankel-Type Transforms (The I, Y and H-Transforms)The Hardy TransformThe K(Meijer)-TransformThe Kontorovich-Lebedev TransformThe Mehler-Fock TransformThe Sturm-Liouville-Type TransformsMiscellaneous Transforms: Kummer, Erdelyi, Hypergeometric, E, and G TransformsThe Bargmann TransformThe Zak TransformThe Gabor TransformThe Ambiguity Transformation and Wigner DistributionThe Wavelet TransformThe Radon TransformSequence Transformations: The Discrete Fourier, Fast Fourier, Z, and Walsh Transforms
Function transforms are some of the most important tools for solving problems in all areas of engineering and the physical sciences. This author compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering.
Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems.
The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included.
The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:
Preliminaries
Special Functions
Generalized Functions
Function Transformations
The Laplace Transform
The Two-Sided Laplace Transform
The Borel Transform
The Stieltjes Transform
The Lambert Transform
The Mellin Transform
The Mellin-Type Transform
The Fourier Transform
The Hartley Transform
The Hilbert Transform
The Boas Transform
The Mittag-Leffler Transform
The Convolution Transform
The Weierstrass Transform
The Abel Transform
The Riemann-Liouville and Weyl Fractional Integrals
The Hankel and Hankel-Type Transforms (The I, Y and H-Transforms)
The Hardy Transform
The K(Meijer)-Transform
The Kontorovich-Lebedev Transform
The Mehler-Fock Transform
The Sturm-Liouville-Type Transforms
Miscellaneous Transforms: Kummer, Erdelyi, Hypergeometric, E, and G Transforms
The Bargmann Transform
The Zak Transform
The Gabor Transform
The Ambiguity Transformation and Wigner Distribution
The Wavelet Transform
The Radon Transform
Sequence Transformations: The Discrete Fourier, Fast Fourier, Z, and Walsh Transforms
Inhaltsverzeichnis
Preliminaries Special Functions Generalized Functions Function Transformations The Laplace Transform The Two-Sided Laplace Transform The Borel Transform The Stieltjes Transform The Lambert Transform The Mellin Transform The Mellin-Type Transform The Fourier Transform The Hartley Transform The Hilbert Transform The Boas Transform The Mittag-Leffler Transform The Convolution Transform The Weierstrass Transform The Abel Transform The Riemann-Liouville and Weyl Fractional Integrals The Hankel and Hankel-Type Transforms (The I, Y and H-Transforms) The Hardy Transform The K(Meijer)-Transform The Kontorovich-Lebedev Transform The Mehler-Fock Transform The Sturm-Liouville-Type Transforms Miscellaneous Transforms: Kummer, Erdelyi, Hypergeometric, E, and G Transforms The Bargmann Transform The Zak Transform The Gabor Transform The Ambiguity Transformation and Wigner Distribution The Wavelet Transform The Radon Transform Sequence Transformations: The Discrete Fourier, Fast Fourier, Z, and Walsh Transforms
Klappentext
Function transforms are some of the important tools for solving problems in all areas of engineering and the physical sciences. This work compiles some of the important and widely used of these function transforms in applied mathematics and electrical engineering.
