Author : Alan M. Cohen
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 23,77 MB
Release : 2007-06-16
Category : Mathematics
ISBN : 0387688552
This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.
Author : Richard Bellman
Publisher : World Scientific
Page : 180 pages
File Size : 24,19 MB
Release : 1984
Category : Mathematics
ISBN : 9789971966737
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.
Author : Urs Graf
Publisher : Birkhäuser
Page : 501 pages
File Size : 38,82 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 303487846X
The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications.
Author : Dean G. Duffy
Publisher : CRC Press
Page : 727 pages
File Size : 25,55 MB
Release : 2004-07-15
Category : Mathematics
ISBN : 1420035142
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana
Author : Joel L. Schiff
Publisher :
Page : 252 pages
File Size : 37,55 MB
Release : 2014-01-15
Category :
ISBN : 9781475772616
Author : Tai-Ran Hsu
Publisher : John Wiley & Sons
Page : 541 pages
File Size : 30,96 MB
Release : 2018-04-30
Category : Technology & Engineering
ISBN : 1119071208
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 : Joel L. Schiff
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 31,85 MB
Release : 2013-06-05
Category : Mathematics
ISBN : 0387227571
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 : Y.H. Gangadharaiah
Publisher : Cambridge Scholars Publishing
Page : 550 pages
File Size : 32,67 MB
Release : 2021-08-25
Category : Mathematics
ISBN : 1527574261
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 : Richard Bellman
Publisher :
Page : 272 pages
File Size : 38,84 MB
Release : 1966
Category : Invariant imbedding
ISBN :
Author : B. Davies
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 50,81 MB
Release : 2013-11-27
Category : Mathematics
ISBN : 1475755120
This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems. It has its im mediate origin in lecture notes prepared for senior level courses at the Australian National University, although I owe a great deal to my colleague Barry Ninham, a matter to which I refer below. In preparing the notes for publication as a book, I have added a considerable amount of material ad- tional to the lecture notes, with the intention of making the book more useful, particularly to the graduate student - volved in the solution of mathematical problems in the physi cal, chemical, engineering and related sciences. Any book is necessarily a statement of the author's viewpoint, and involves a number of compromises. My prime consideration has been to produce a work whose scope is selective rather than encyclopedic; consequently there are many facets of the subject which have been omitted--in not a few cases after a preliminary draft was written--because I v believe that their inclusion would make the book too long.
