Laplace Transforms Essentials

2013-01-01
Laplace Transforms Essentials

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  • Author: Morteza Shafii-Mousavi
  • Publisher: Research & Education Assoc.
  • ISBN: 0738672459
  • Category : Mathematics
  • Languages : en
  • Pages : 188

REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Laplace Transforms includes the Laplace transform, the inverse Laplace transform, special functions and properties, applications to ordinary linear differential equations, Fourier transforms, applications to integral and difference equations, applications to boundary value problems, and tables.

Tables of Laplace Transforms

2012-12-06
Tables of Laplace Transforms

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  • Author: F. Oberhettinger
  • Publisher: Springer Science & Business Media
  • ISBN: 3642656455
  • Category : Mathematics
  • Languages : en
  • Pages : 438

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

The Laplace Transform

1984
The Laplace Transform

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  • Author: Richard Bellman
  • Publisher: World Scientific
  • ISBN: 9789971966737
  • Category : Mathematics
  • Languages : en
  • Pages : 180

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.

An Introduction to Laplace Transforms and Fourier Series

2012-12-06
An Introduction to Laplace Transforms and Fourier Series

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  • Author: P.P.G. Dyke
  • Publisher: Springer Science & Business Media
  • ISBN: 1447105052
  • Category : Mathematics
  • Languages : en
  • Pages : 257

This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.

Laplace Transform (PMS-6)

2015-12-08
Laplace Transform (PMS-6)

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  • Author: David Vernon Widder
  • Publisher: Princeton University Press
  • ISBN: 1400876451
  • Category : Mathematics
  • Languages : en
  • Pages : 417

Book 6 in the Princeton Mathematical Series. Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Fourier and Laplace Transforms

2003-08-07
Fourier and Laplace Transforms

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  • Author:
  • Publisher: Cambridge University Press
  • ISBN: 9780521534413
  • Category : Mathematics
  • Languages : en
  • Pages : 468

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.

Complex Variables and the Laplace Transform for Engineers

2012-04-26
Complex Variables and the Laplace Transform for Engineers

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  • Author: Wilbur R. LePage
  • Publisher: Courier Corporation
  • ISBN: 0486136442
  • Category : Technology & Engineering
  • Languages : en
  • Pages : 516

Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

Laplace Transforms

1973
Laplace Transforms

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  • Author: K. A. Stroud
  • Publisher:
  • ISBN:
  • Category : Mathematics
  • Languages : en
  • Pages : 294

The Laplace Transform

2014-01-15
The Laplace Transform

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  • Author: Joel L. Schiff
  • Publisher:
  • ISBN: 9781475772616
  • Category :
  • Languages : en
  • Pages : 252

Vector-valued Laplace Transforms and Cauchy Problems

2013-11-11
Vector-valued Laplace Transforms and Cauchy Problems

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  • Author: Wolfgang Arendt
  • Publisher: Springer Science & Business Media
  • ISBN: 3034850751
  • Category : Mathematics
  • Languages : en
  • Pages : 526

Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .