*Theory and Applications*

Author: Bill Goodwine

Publisher: Springer Science & Business Media

ISBN: 1441979190

Category: Mathematics

Page: 745

View: 6089

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### Engineering Differential Equations

This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

### ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

This revised and updated text, now in its second edition, continues to present the theoretical concepts of methods of solutions of ordinary and partial differential equations. It equips students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of ordinary and partial differential equations. It contains different methods of solving ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The text elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel’s and Legendre’s equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics. New to the SECOND Edition • Includes new sections and subsections such as applications of differential equations, special substitution (Lagrange and Riccati), solutions of non-linear equations which are exact, method of variation of parameters for linear equations of order higher than two, and method of undetermined coefficients • Incorporates several worked-out examples and exercises with their answers • Contains a new Chapter 19 on ‘Z-Transforms and its Applications’.

### Differential Equations: Theory and Applications

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. The accompanying CD contains Maple worksheets for the exercises, and special Maple code for performing various tasks. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.

### Partielle Differentialgleichungen der Geometrie und der Physik 1

### Theory and Applications of Partial Differential Equations

This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

### Partielle Differentialgleichungen der Geometrie und der Physik 2

Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

### Decomposition Methods for Differential Equations

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results. The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB®, R3T, WIAS-HiTNIHS, and OPERA-SPLITT. Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems.

### Ordinary Differential Equations with Applications

This graduate-level textbook offers students a rapid introduction to the language of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering.

### Optimale Steuerung partieller Differentialgleichungen

Die mathematische Theorie der optimalen Steuerung hat sich im Zusammenhang mit Berechnungen für die Luft- und Raumfahrt schnell zu einem wichtigen und eigenständigen Gebiet der angewandten Mathematik entwickelt. Die optimale Steuerung durch partielle Differentialgleichungen modellierter Prozesse wird eine numerische Herausforderung der Zukunft sein. Sie erfordert die Analysis nichtlinearer partieller Differentialgleichungen, Optimierung im Funktionenraum, nichtlineare Funktionalanalysis sowie Optimierungsverfahren für extrem große Aufgaben. Im Buch werden entsprechende Grundlagen mit langsam steigendem Schwierigkeitsgrad entwickelt. Grundkenntnisse zu partiellen Differentialgleichungen und der Funktionalanalysis werden jeweils dort gebracht, wo sie konkret nötig sind. Das Buch enthält viele Beispiele und eignet sich als Grundlage für Vorlesungen und Seminare.

### DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

Primarily intended for the undergraduate students of mathematics, physics and engineering, this text gives in-depth coverage of differential equations and the methods for solving them. The book begins with the definitions, the physical and geometric origins of differential equations, and the methods for solving the first order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher order differential equations and their applications to telecommunications, civil engineering, cardiology and detection of diabetes, as also the methods of solving simultaneous differential equations and their applications. Besides, the book provides a detailed discussion on Laplace transforms and their applications, partial differential equations and their applications to vibration of stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. The book, which is a happy fusion of theory and application, would also be useful to postgraduate students.NEW TO THIS EDITION • New sections on: (a) Equations reducible to linear partial differential equations (b) General method for solving the second order non-linear partial differential equations (Monge’s Method) (c) Lagrange’s equations of motion • Number of solved examples in Chapters 5, 7, 8, 9 and 10.

### ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS : THEORY AND APPLICATIONS

This book presents the theoretical concepts of methods of solutions of ordinary and partial differential equations as well as equips the students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of differential equations, different methods of solving ordinary differential equations and the solution procedure for ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The book elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel's and Legendre's equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics.

### Differential Equations for Engineers

Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.

### Introduction to the Theory and Application of Differential Equations with Deviating Arguments

Introduction to the Theory and Application of Differential Equations with Deviating Arguments 2nd edition is a revised and substantially expanded edition of the well-known book of L. E. El’sgol’ts published under this same title by Nauka in 1964. Extensions of the theory of differential equations with deviating argument as well as the stimuli of developments within various fields of science and technology contribute to the need for a new edition. This theory in recent years has attracted the attention of vast numbers of researchers, interested both in the theory and its applications. The development of the foundations of the theory of differential equations with a deviating argument is still far from complete. This situation, of course, leaves its mark on our suggestions to the reader of the book and prevents as orderly and systematic a presentation as is usual for mathematical literature. However, it is hoped that in spite of these deficiencies the book will prove useful as a first acquaintanceship with the theory of differential equations with a deviating argument.

### Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

### Theory of Stochastic Differential Equations with Jumps and Applications

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

### Ordinary Differential Equations

This introductory course in ordinary differential equations, intended for junior undergraduate students in applied mathematics, science and engineering, focuses on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering. The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained. To promote the use of this course for self-study, suggested solutions are not only given to all set exercises, but they are also by and large complete with details.

### Stochastic Differential Equations

Practical and not too rigorous, this highly readable text on stochastic calculus provides an excellent introduction to stochastic partial differential equations. Written at a moderately advanced level, it covers important topics often ignored by other texts on the subject—including Fokker-Planck equations—and it functions as both a classroom text and a reference for professionals and students. The only prerequisite is the mathematical preparation usual for students of physical and engineering sciences. An introductory chapter, intended for reference and review, covers the basics of probability theory. Subsequent chapters focus on Markov and diffusion processes, Wiener process and white noise, and stochastic integrals and differential equations. Additional topics include questions of modeling and approximation, stability of stochastic dynamic systems, optimal filtering of a disturbed signal, and optimal control of stochastic dynamic systems.

### Partial Differential Equations

Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

### Introduction to the Theory and Applications of Functional Differential Equations

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.

### Stochastic Differential Equations

'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl!be~ IbcII _t to!be dusty cauialcr Iabc & d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely.

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Publisher: Springer Science & Business Media

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Page: 745

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