Introduction To The Theory And Application Of The Laplace Transformation

Author : Gustav Doetsch,Walter Nader
Publisher : Springer
Page : 326 pages
File Size : 42,5 Mb
Release : 1974
Category : Laplace transformation
ISBN : 3540064079

Get Book

Introduction to the Theory and Application of the Laplace Transformation by Gustav Doetsch,Walter Nader Pdf

In anglo-american literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi­ nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, presuming special properties with respect to the transformed func­ tions, which allow easy proofs. By contrast, the present book intends principally to develop those parts of the theory of the Laplace transformation, which are needed by mathematicians, physicists a,nd engineers in their daily routine work, but in complete generality and with detailed, exact proofs. The applications to other mathematical domains and to technical prob­ lems are inserted, when the theory is adequately· developed to present the tools necessary for their treatment. Since the book proceeds, not in a rigorously systematic manner, but rather from easier to more difficult topics, it is suited to be read from the beginning as a textbook, when one wishes to familiarize oneself for the first time with the Laplace transforma­ tion. For those who are interested only in particular details, all results are specified in "Theorems" with explicitly formulated assumptions and assertions. Chapters 1-14 treat the question of convergence and the mapping properties of the Laplace transformation. The interpretation of the transformation as the mapping of one function space to another (original and image functions) constitutes the dom­ inating idea of all subsequent considerations.

Author : Gustav Doetsch
Publisher : Unknown
Page : 326 pages
File Size : 46,5 Mb
Release : 1970
Category : Laplace transformation
ISBN : OCLC:217173946

Get Book

Introduction to the Theory and Application of the Laplace Transformation by Gustav Doetsch Pdf

Author : Anonim
Publisher : Academic Press
Page : 272 pages
File Size : 45,5 Mb
Release : 1971-09-30
Category : Mathematics
ISBN : 9780080873558

Get Book

An introduction to transform theory by Anonim Pdf

An introduction to transform theory

Author : G. Doetsch
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642656903

Get Book

Introduction to the Theory and Application of the Laplace Transformation by G. Doetsch Pdf

In anglo-american literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, presuming special properties with respect to the transformed func tions, which allow easy proofs. By contrast, the present book intends principally to develop those parts of the theory of the Laplace transformation, which are needed by mathematicians, physicists a,nd engineers in their daily routine work, but in complete generality and with detailed, exact proofs. The applications to other mathematical domains and to technical prob lems are inserted, when the theory is adequately· developed to present the tools necessary for their treatment. Since the book proceeds, not in a rigorously systematic manner, but rather from easier to more difficult topics, it is suited to be read from the beginning as a textbook, when one wishes to familiarize oneself for the first time with the Laplace transforma tion. For those who are interested only in particular details, all results are specified in "Theorems" with explicitly formulated assumptions and assertions. Chapters 1-14 treat the question of convergence and the mapping properties of the Laplace transformation. The interpretation of the transformation as the mapping of one function space to another (original and image functions) constitutes the dom inating idea of all subsequent considerations.

Author : Joel L. Schiff
Publisher : Unknown
Page : 252 pages
File Size : 41,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475772610

Get Book

The Laplace Transform by Joel L. Schiff Pdf

Author : Peter K.F. Kuhfittig
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 44,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489922014

Get Book

Introduction to the Laplace Transform by Peter K.F. Kuhfittig Pdf

The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.

Author : Joel L. Schiff
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 53,7 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780387227573

Get Book

The Laplace Transform by Joel L. Schiff Pdf

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.

Author : Vladimir Eiderman
Publisher : CRC Press
Page : 383 pages
File Size : 46,6 Mb
Release : 2021-12-20
Category : Mathematics
ISBN : 9781000511123

Get Book

An Introduction to Complex Analysis and the Laplace Transform by Vladimir Eiderman Pdf

The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book. This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses. In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well. A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms. Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.

Author : Tai-Ran Hsu
Publisher : John Wiley & Sons
Page : 541 pages
File Size : 52,9 Mb
Release : 2018-04-30
Category : Technology & Engineering
ISBN : 9781119071204

Get Book

Applied Engineering Analysis by Tai-Ran Hsu Pdf

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.

Author : John Conrad Jaeger,Gordon Newstead
Publisher : Unknown
Page : 168 pages
File Size : 48,9 Mb
Release : 1969
Category : Integral transforms
ISBN : UOM:39015017335822

Get Book

An Introduction to the Laplace Transformation by John Conrad Jaeger,Gordon Newstead Pdf

Author : N.W. McLachlan
Publisher : Courier Corporation
Page : 241 pages
File Size : 53,9 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9780486798233

Get Book

Laplace Transforms and Their Applications to Differential Equations by N.W. McLachlan Pdf

Classic graduate-level exposition covers theory and applications to ordinary and partial differential equations. Includes derivation of Laplace transforms of various functions, Laplace transform for a finite interval, and more. 1948 edition.

Author : Y.H. Gangadharaiah,N. Sandeep
Publisher : Cambridge Scholars Publishing
Page : 550 pages
File Size : 55,8 Mb
Release : 2021-08-25
Category : Mathematics
ISBN : 9781527574267

Get Book

Engineering Applications of the Laplace Transform by Y.H. Gangadharaiah,N. Sandeep Pdf

This book is devoted to one of the most critical areas of applied mathematics, namely the Laplace transform technique for linear time invariance systems arising from the fields of electrical and mechanical engineering. It focuses on introducing Laplace transformation and its operating properties, finding inverse Laplace transformation through different methods, and describing transfer function applications for mechanical and electrical networks to develop input and output relationships. It also discusses solutions of initial value problems, the state-variables approach, and the solution of boundary value problems connected with partial differential equations.

Author : John Conrad Jaeger
Publisher : Unknown
Page : 172 pages
File Size : 46,8 Mb
Release : 1961
Category : Laplace transformation
ISBN : UVA:X001322407

Get Book

An Introduction to the Laplace Transformations by John Conrad Jaeger Pdf

Author : P.P.G. Dyke
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105053

Get Book

An Introduction to Laplace Transforms and Fourier Series by P.P.G. Dyke Pdf

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.

Author : J. L. Schiff
Publisher : Unknown
Page : 250 pages
File Size : 42,5 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:808037099

Get Book

The Laplace Transform by J. L. Schiff Pdf

The Laplace transform is a wonderful tool for solving ordinary and partial differential equations, and has enjoyed much success in this realm. In the present text, the author brings to the subject a certain amount of mathematical correctness and makes it accessible to undergraduates.