Tables of Laplace Transforms

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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 Laplace Transforms

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ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Tables of Laplace Transforms by : Bertrand Julian Starkey

Download or read book Tables of Laplace Transforms written by Bertrand Julian Starkey and published by . This book was released on 1957 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Table of Laplace Transforms

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ISBN 13 :
Total Pages : 412 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 1968 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tables of Integral Transforms

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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:

Handbook of Laplace Transformation

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ISBN 13 :
Total Pages : 314 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Handbook of Laplace Transformation by : Floyd E. Nixon

Download or read book Handbook of Laplace Transformation written by Floyd E. Nixon and published by . This book was released on 1965 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Table of LaPlace Transforms. Revised Edition

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ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Table of LaPlace Transforms. Revised Edition by : E. C. Levy

Download or read book Table of LaPlace Transforms. Revised Edition written by E. C. Levy and published by . This book was released on 1953 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report contains mathematical tables of Laplace transformations.

Tables of Laplace Transforms

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ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Tables of Laplace Transforms by : William David Day

Download or read book Tables of Laplace Transforms written by William David Day and published by . This book was released on 1966 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tables of Coefficients for the Numerical Calculation of Laplace Transforms

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ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Tables of Coefficients for the Numerical Calculation of Laplace Transforms by : Herbert E. Salzer

Download or read book Tables of Coefficients for the Numerical Calculation of Laplace Transforms written by Herbert E. Salzer and published by . This book was released on 1953 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tables of Mellin Transforms

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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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tables of Laplace Transforms [By] Fritz Oberhettinger [And] Larry Badii

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ISBN 13 :
Total Pages : 428 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Tables of Laplace Transforms [By] Fritz Oberhettinger [And] Larry Badii by : Fritz Oberhettinger

Download or read book Tables of Laplace Transforms [By] Fritz Oberhettinger [And] Larry Badii written by Fritz Oberhettinger and published by . This book was released on 1973 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A New Table of Laplace Transformation Pairs

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ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A New Table of Laplace Transformation Pairs by : Ezra C. Levy

Download or read book A New Table of Laplace Transformation Pairs written by Ezra C. Levy and published by . This book was released on 1963 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Table of Integrals, Series, and Products

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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.

Tables of Bessel Transforms

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Publisher : Springer Science & Business Media
ISBN 13 : 3642654622
Total Pages : 299 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Tables of Bessel Transforms by : F. Oberhettinger

Download or read book Tables of Bessel Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This material represents a collection of integral tra- forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy) 2 [Iv (xy) + I_v(xy)]dy J 27fT c-ioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV' - f(x) J v 0 V Preface V. g(y) f(X)Kix(y)dx J 0 -2 -1 sinh (7TX) V'. f(x) 27T x g(y)y Kix(y)dy J 0 21-~[r(~~+~-~v)r(~~+~+~v)]-1 VI. g(y) . J f (x) (xy) ~s (xy) dx o ~, v l-~ -1 VI' . f(x) 2 [r (~~+~-~v) r (~~+~+~v)] - - J -5 (xy)]dy g(y) (XY)~[S~, v(xy) ~, v 0 [xy)~]dX VII. g(y) f(x)\ ~ J 0 0 VII' - f(x) g(y) \ [(xy) lz]dy ~ f 0 0 with \ (z) o (For notations and definitions see the appendix of this book.) The transform VII is also known as the divisor transform.

Table of Laplace Transforms

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ISBN 13 :
Total Pages : 428 pages
Book Rating : 4.:/5 (976 download)

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Book Synopsis Table of Laplace Transforms by :

Download or read book Table of Laplace Transforms written by and published by . This book was released on 1973 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tables of Laplace Transforms. Reprinted from (appendix C Of) Laplace Transforms for Electrical Engineers

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ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (314 download)

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Book Synopsis Tables of Laplace Transforms. Reprinted from (appendix C Of) Laplace Transforms for Electrical Engineers by : Bertrand Julian Starkey

Download or read book Tables of Laplace Transforms. Reprinted from (appendix C Of) Laplace Transforms for Electrical Engineers written by Bertrand Julian Starkey and published by . This book was released on 1957 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Laplace Transform

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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

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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.