A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation

V.I. Krylov; N.S. Skoblya; George Yankovsky [translator from the Russian]

Published by Mir Publishers, Moscow, 1985

About this Item

Scarce small-format hardcover 17 x 13 x 2 cm, 271 pages, revised from the 1974 Russian edition, second printing, NOT ex-library. No ISBN. Clean, bright, untanned interior with unmarked text, firmly bound. Boards show regular shelfwear and faint handling marks. Spine is slightly leaned with short creases to upper/lower ends. Issued without a dust jacket. -- Harmonic analysis and the Laplace transformation are tools that are frequently used to solve a wide range of theoretical and applied problems. This text contains most of the familiar methods of approximate inversion of the Laplace transformation and calculation of Fourier integrals. This book is designed for scientists and engineers that have to deal with the theory and applications of the Laplace transform and Fourier integrals. It will be a useful handbook in every computer centre and designing bureau. -- Contents: List of Symbols; Preface; Part 1: Inversion of the Laplace Transformation 1. Introduction [Basic Concepts in the Theory of the Laplace Transformation; Complex Integral for Computing Inverse Laplace Transforms; Representing Functions by the Laplace Integral; Ill-Conditioning of the Problem of Computing Inverse Laplace Transforms] 2. Some Analytical Methods for Computing Inverse Laplace Transforms [Finding the Original Function via the Inversion Formula; Expanding the Original Function into Power Series; Expanding the Original Function into Generalized Power Series] 3. Methods of Numerical Inversion of Laplace Transforms Based on the Use of Special Expansions [Computing Inverse Laplace Transforms by Polynomials Orthogonal on a Finite Interval; Computing Inverse Laplace Transforms with the Aid of the Fourier Sine Series; Computing Inverse Laplace Transforms with the Aid of Series in Terms of Generalized Chebyshev- Laguerre Polynomials] 4. Methods of Computing the Mellin Integral with the Aid of Interpolation Quadrature Formulas [General Theory of Interpolation Methods; Equal-Interval Interpolation Method; Unequal-Interval Interpolation Method; Other Interpolation Methods. Using the Truncated Taylor Series; Some Theorems on Convergence of Interpolation; Theorems on the Convergence of Interpolation Methods of Inversion] 5. Methods of Numerical Inversion of Laplace Transforms via Quadrature Formulas of Highest Accuracy [Theory of Quadrature Formulas; Orthogonal Polynomials Connected with the Quadrature Formula of Highest Accuracy; Methods for Computing the Coefficients and Points of a Quadrature Formula] 6. Methods of Inverting Laplace Transforms via Quadrature Formulas with Equal Coefficients [Constructing a Computation Formula; Remark on the Spacing of Points]; Part 2: Fourier Transforms and Their Application to Inversion of Laplace Transforms 7. Introduction [Fourier Transforms; Reducing Integrals of the Mellin Type to the Fourier Transformation] 8. Inversion of Laplace Transforms by Means of the Fourier Series [Case of a Rapidly Decreasing Original Function f (x); Case of Rapid Decrease of the Modulus of the Image Function F (p)] 9. Interpolation Formulas for Computing Fourier Integrals [Some Preliminary Remarks; Algebraic Interpolation of the Function f (x); Interpolation by Rational Functions] 10. Highest-Accuracy Formulas for Computation [Introduction; Constructing a Formula of Highest Degree of Accuracy]; Part 3: Isolating Singularities of a Function in Computations 11. Isolating Singularities of the Image Function F (p) [Introduction; Removing and Weakening the Singularities of the Image Function F (p); A Remark on the Increase in the Rate of Approach to zero of the Image Function F (p); A Table of Image Functions F (p) and the Corresponding Original Functions f (x) for Constructing the Singular Part of the Image Function F1 (p)] 12. Isolating Singularities of a Function in the Fourier Transformation [Removing Discontinuities of the First Kind; Increasing the Rate of Approach to Zero of the Function Undergoing Transformation]; Bibliography; Index.

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Bibliographic Details

• Title: A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation
• Publisher: Mir Publishers, Moscow
• Publication Date: 1985
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: Very Good