Author: Reza N. Jazar Publisher: Springer Nature ISBN: 3030734625 Category : Technology & Engineering Languages : en Pages : 584
Book Description
Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.
Author: Anatoli V. Skorokhod Publisher: Springer Science & Business Media ISBN: 0387224467 Category : Mathematics Languages : en Pages : 500
Book Description
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Author: Richard Ernest Bellman Publisher: Courier Corporation ISBN: 9780486432588 Category : Science Languages : en Pages : 146
Book Description
Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.
Author: İlkay Bakırtaş Publisher: BoD – Books on Demand ISBN: 1789842557 Category : Mathematics Languages : en Pages : 170
Book Description
The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.
Author: Carl M. Bender Publisher: Springer Science & Business Media ISBN: 1475730691 Category : Mathematics Languages : en Pages : 605
Book Description
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Author: Wenfang Chen Publisher: World Scientific ISBN: 9789810237271 Category : Mathematics Languages : en Pages : 272
Book Description
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
Author: Alan W. Bush Publisher: CRC Press ISBN: 9780849386084 Category : Mathematics Languages : en Pages : 326
Book Description
Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid dynamics applications, including aerofoils, boundary layers in momentum heat, and mass transfer. In addition, it applies the multiple scale technique to the description of surface roughness effects in lubrication. The book's intuitive, rather than formal, approach enables these advanced techniques to be used by scientists and engineers as well as by students.
Author: R.S. Johnson Publisher: Springer Science & Business Media ISBN: 0387232176 Category : Technology & Engineering Languages : en Pages : 292
Book Description
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.
Author: J.K. Kevorkian Publisher: Springer Science & Business Media ISBN: 1461239680 Category : Mathematics Languages : en Pages : 642
Book Description
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
Author: Reza N. Jazar
Author: Anatoli V. Skorokhod
Author: Richard Ernest Bellman
Author: İlkay Bakırtaş
Author: Carl M. Bender
Author: Wenfang Chen
Author: Alan W. Bush
Author: R.S. Johnson
Author: J.K. Kevorkian
Author: Mihail M. Konstantinov