Tables Of Laplace Transforms

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Tables of Laplace Transforms

Author : F. Oberhettinger
Publisher : Springer Science & Business Media
ISBN 13 : 3642656455
Total Pages : 438 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Tables of Laplace Transforms by : F. Oberhettinger

Download or read book Tables of Laplace Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This material represents a collection of integrals of the Laplace- and inverse Laplace Transform type. The usef- ness of this kind of information as a tool in various branches of Mathematics is firmly established. Previous publications include the contributions by A. Erdelyi and Roberts and Kaufmann (see References). Special consideration is given to results involving higher functions as integrand and it is believed that a substantial amount of them is presented here for the first time. Greek letters denote complex parameters within the given range of validity. Latin letters denote (unless otherwise stated) real positive parameters and a possible extension to complex values by analytic continuation will often pose no serious problem. The authors are indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manu script. Oregon State University Corvallis, Oregon Eastern Michigan University Ypsilanti, Michigan The Authors Contents Part I. Laplace Transforms In troduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 Algebraic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 3 Powers of Arbitrary Order. . . . . . . . . . . . . . . . . . . . . . . . 21 1. 4 Sectionally Rational- and Rows of Delta Functions 28 1. 5 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1. 6 Logarithmic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 1. 7 Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . 54 1. 8 Inverse Trigonometric Functions. . . . . . . . . . . . . . . . . . 81 1. 9 Hyperbolic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 1. 10 Inverse Hyperbolic Functions. . . . . . . . . . . . . . . . . . . . . 99 1. 11 Orthogonal Polynomials . . . . . . . •. . . . . . . . . . . . . . . . . . . 103 1. 12 Legendre Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 1. 13 Bessel Functions of Order Zero and Unity . . . . . . . . . 119 1. 14 Bessel Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 1. 15 Modified Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . .

Tables of Integral Transforms

Author : Bateman Manuscript Project
Publisher :
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Tables of Integral Transforms by : Bateman Manuscript Project

Download or read book Tables of Integral Transforms written by Bateman Manuscript Project and published by . This book was released on 1954 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tables of Mellin Transforms

Author : F. Oberhettinger
Publisher : Springer Science & Business Media
ISBN 13 : 3642659756
Total Pages : 284 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Tables of Mellin Transforms by : F. Oberhettinger

Download or read book Tables of Mellin Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions conce~ning Mellin trans forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . • . • • • . • . . . . . . . . . . . . • • • • . . . • . • . . • • • . • . 1 Some Applications of the Mellin Transform Analysis. ••. •••. . . •. •. . . . •• . • . . . . . . ••. . . . . •• 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table of Integrals, Series, and Products

Author : I. S. Gradshteyn
Publisher : Academic Press
ISBN 13 : 1483265641
Total Pages : 1207 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Table of Integrals, Series, and Products by : I. S. Gradshteyn

Download or read book Table of Integrals, Series, and Products written by I. S. Gradshteyn and published by Academic Press. This book was released on 2014-05-10 with total page 1207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Table of Integrals, Series, and Products

Author : Daniel Zwillinger
Publisher : Elsevier
ISBN 13 : 0080471110
Total Pages : 1220 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Table of Integrals, Series, and Products by : Daniel Zwillinger

Download or read book Table of Integrals, Series, and Products written by Daniel Zwillinger and published by Elsevier. This book was released on 2007-02-23 with total page 1220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with text- Most up to date listing of integrals, series andproducts - Provides accuracy and efficiency in work

The Laplace Transform

Author : Joel L. Schiff
Publisher : Springer Science & Business Media
ISBN 13 : 0387227571
Total Pages : 245 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Laplace Transform by : Joel L. Schiff

Download or read book The Laplace Transform written by Joel L. Schiff and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.

Applied Engineering Analysis

Author : Tai-Ran Hsu
Publisher : John Wiley & Sons
ISBN 13 : 1119071208
Total Pages : 541 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Applied Engineering Analysis by : Tai-Ran Hsu

Download or read book Applied Engineering Analysis written by Tai-Ran Hsu and published by John Wiley & Sons. This book was released on 2018-04-30 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls. Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors. Key features: Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student’s self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC). Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.

Laplace Transforms for Electronic Engineers

Author : James G. Holbrook
Publisher : Elsevier
ISBN 13 : 1483185656
Total Pages : 365 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Laplace Transforms for Electronic Engineers by : James G. Holbrook

Download or read book Laplace Transforms for Electronic Engineers written by James G. Holbrook and published by Elsevier. This book was released on 2014-05-16 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laplace Transforms for Electronic Engineers, Second (Revised) Edition details the theoretical concepts and practical application of Laplace transformation in the context of electrical engineering. The title is comprised of 10 chapters that cover the whole spectrum of Laplace transform theory that includes advancement, concepts, methods, logic, and application. The book first covers the functions of a complex variable, and then proceeds to tackling the Fourier series and integral, the Laplace transformation, and the inverse Laplace transformation. The next chapter details the Laplace transform theorems. The subsequent chapters talk about the various applications of the Laplace transform theories, such as network analysis, transforms of special waveshapes and pulses, electronic filters, and other specialized applications. The text will be of great interest to electrical engineers and technicians.

CRC Standard Mathematical Tables and Formulae, 32nd Edition

Author : Daniel Zwillinger
Publisher : CRC Press
ISBN 13 : 1439835500
Total Pages : 792 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis CRC Standard Mathematical Tables and Formulae, 32nd Edition by : Daniel Zwillinger

Download or read book CRC Standard Mathematical Tables and Formulae, 32nd Edition written by Daniel Zwillinger and published by CRC Press. This book was released on 2011-06-22 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material. New to the 32nd Edition A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics New material on contingency tables, estimators, process capability, runs test, and sample sizes New material on cellular automata, knot theory, music, quaternions, and rational trigonometry Updated and more streamlined tables Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.

Table of Laplace Transforms

Author : George E. Roberts
Publisher :
ISBN 13 :
Total Pages : 434 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Table of Laplace Transforms by : George E. Roberts

Download or read book Table of Laplace Transforms written by George E. Roberts and published by . This book was released on 1966 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Formulas and Tables for Signal Processing

Author : Alexander D. Poularikas
Publisher : CRC Press
ISBN 13 : 9781420049701
Total Pages : 872 pages
Book Rating : 4.0/5 (497 download)

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Book Synopsis Handbook of Formulas and Tables for Signal Processing by : Alexander D. Poularikas

Download or read book Handbook of Formulas and Tables for Signal Processing written by Alexander D. Poularikas and published by CRC Press. This book was released on 1998-09-29 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signal processing is a broad and timeless area. The term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical, and more. Signal processing applies to the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals. Handbook of Formulas and Tables for Signal Processing a must-have reference for all engineering professionals involved in signal and image processing. Collecting the most useful formulas and tables - such as integral tables, formulas of algebra, formulas of trigonometry - the text includes: Material for the deterministic and statistical signal processing areas Examples explaining the use of the given formula Numerous definitions Many figures that have been added to special chapters Handbook of Formulas and Tables for Signal Processing brings together - in one textbook - all the equations necessary for signal and image processing for professionals transforming anything from a physical to a manipulated form, creating a new standard for any person starting a future in the broad, extensive area of research.

The Laplace Transform

Author : Richard Bellman
Publisher : World Scientific
ISBN 13 : 9789971966737
Total Pages : 180 pages
Book Rating : 4.9/5 (667 download)

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Book Synopsis The Laplace Transform by : Richard Bellman

Download or read book The Laplace Transform written by Richard Bellman and published by World Scientific. This book was released on 1984 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.

Notes on Diffy Qs

Author : Jiri Lebl
Publisher :
ISBN 13 : 9781706230236
Total Pages : 468 pages
Book Rating : 4.2/5 (32 download)

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Book Synopsis Notes on Diffy Qs by : Jiri Lebl

Download or read book Notes on Diffy Qs written by Jiri Lebl and published by . This book was released on 2019-11-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

Handbook of Mathematical Functions

Author : Milton Abramowitz
Publisher : Courier Corporation
ISBN 13 : 9780486612720
Total Pages : 1068 pages
Book Rating : 4.6/5 (127 download)

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Book Synopsis Handbook of Mathematical Functions by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

Author : Milton Abramowitz
Publisher :
ISBN 13 :
Total Pages : 1072 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables written by Milton Abramowitz and published by . This book was released on 1964 with total page 1072 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fourier and Laplace Transforms

Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521534413
Total Pages : 468 pages
Book Rating : 4.5/5 (344 download)

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Book Synopsis Fourier and Laplace Transforms by :

Download or read book Fourier and Laplace Transforms written by and published by Cambridge University Press. This book was released on 2003-08-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Local Fractional Integral Transforms and Their Applications

Author : Xiao-Jun Yang
Publisher : Academic Press
ISBN 13 : 0128040327
Total Pages : 263 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Local Fractional Integral Transforms and Their Applications by : Xiao-Jun Yang

Download or read book Local Fractional Integral Transforms and Their Applications written by Xiao-Jun Yang and published by Academic Press. This book was released on 2015-10-22 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. - Provides applications of local fractional Fourier Series - Discusses definitions for local fractional Laplace transforms - Explains local fractional Laplace transforms coupled with analytical methods