Springer, 2022. — 287 p. This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: Approximate symmetry in nonlinear physical problems Complex methods for Lie symmetry analysis Lie group classification, Symmetry analysis, and conservation laws Conservative difference schemes Hamiltonian structure and conservation...
World Scientific, 2015. — 245 p. This book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation. In 1967, Andrzej Lasota and Zdzisław Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two...
CRC Press, 2022. — 488 p. — Third Edition. Differential equations is one of the oldest subjects in modern mathematics. It was not long after Newton and Leibniz invented the calculus that Bernoulli and Euler and others began to consider the heat equation and the wave equation of mathematical physics. Newton himself solved differential equations both in the study of planetary...
Springer, 2021. — 339 p. This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed....
Springer, 2021. — 467 p. The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza"....
12th Edition. — Wiley, 2022. — 640 p. The book is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. In this revision, new author Douglas Meade focuses on developing students conceptual understanding with new concept questions and...
World Scientific, 2018. — 121 p. The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book.The authors begin with a study of initial...
Springer, 2023. — 609 p. The textbook presents a rather unique combination of topics in ODEs, examples and presentation style. The primary intended audience is undergraduate (2nd, 3rd, or 4th year) students in engineering and science (physics, biology, economics). The needed pre-requisite is a mastery of single-variable calculus. A wealth of included topics allows using the...
Учебное пособие. — М.: Московская государственная академия водного транспорта (МГАВТ), 2019. — 92 с. Курс лекций по дифференциальному исчислению подготовлен доцентом кафедры Естественнонаучных и математических дисциплин Московской государственной академии водного транспорта, кандидатом технических наук В.А. Логиновым. Лекции предназначены для студентов МГАВТ, обучающихся по...
CRC Press, 2020. — 394 p. Higher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the...
CRC Press, 2020. — 326 p. Simultaneous Differential Equations and Multi-Dimensional Vibrations is the fourth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This fourth book consists of two chapters (chapters...
Birkhauser, 2020. — 347 p. This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent...
Оренбург: ОГУ, 2013. — 59 с. Методические указания посвящены решению обыкновенных дифференциальных уравнений и прикладных задач, приводящих к ним, и предназначены для проведения практических занятий по дисциплине «Дифференциальные уравнения». Методические указания включают теоретические сведения по дифференциальным уравнениям, примеры решений задач, задания для самостоятельного...
Bookboon, 2014. — 57 p. This book, together with the linked YouTube videos, reviews a first course on differential equations. The main purpose is to help students prepare for their university exams. Theory is summarized, and the solutions of typical exam questions are demonstrated in YouTube videos. Additional practice questions are given and their solutions are presented in the...
Bookboon, 2015. — 168 p. This book is aimed at students who encounter mathematical models in other disciplines. It assumes some knowledge of calculus, and explains the tools and concepts for analysing models involving sets of either algebraic or 1st order differential equations. The text emphasises commonalities between these modelling approaches. The approach is practical, aiming...
Bookboon, 2015. — 232 p. The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, including general vector spaces and integral calculus for functions of one variable. No knowledge of differential equations is required to read and...
Springer, 2017. — 245 p. There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural...
Springer, 2015. — 323 p. There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural...
Springer, 2013. — 243 p. Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers...
Springer, 2008. — 404 p. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical...
Springer, 2003. — 471 p. Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest,...
Springer, 2005. — 306 p. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical...
Kluwer, 1991. — 360 p. — ISBN: 9780792303817, 0792303814. The book deals with the theory of boundary value problems for second-order operator differential equations. The book provides a number of examples which prove that the operator approach makes it possible not only to extend the class of already studied partial differential equations and their boundary value problems, but...
North-Holland, 1983. — 477 p. Nonlinear equations come to us in tremendous variety, each with its own questions and its own difficulties. At one extreme are the completely integrable equations, with constants of the motion and a rich algebraic structure. At the other extreme is chaos, with turbulent solutions and statistical averages. Between these two possibilities, algebraic...
Kluwer, 1988. — 325 p. Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders....
Springer, 1977. — 512 p. Elementary Methods for Ordinary Differential Equations of First Order Uniqueness and Lipschitz Conditions for Ordinary Differential Equations The Linear Ordinary Equation of Order n Linear Ordinary Differential Systems Introduction to Delay Differential Equations Existence Theory Linear Delay Differential Systems Stability Autonomous Ordinary...
Springer, 1980. — 575 p. The prime purpose of the present monograph is the presentation of a historical and comprehensive survey of the Sturmian theory for self-adjoint differential systems, and for this purpose the classical Sturmian theory is but an important special instance. On the othej hand, it is felt that the Sturmian theory for a single real self-adjoint linear...
Springer, 2014. — 321 p. Particle Systems and PDEs, Braga, Portugal, December 2012. This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012. The purpose of the conference was to bring...
Springer, 2015. — 395 p. Particle Systems and PDEs II, Braga, Portugal, December 2013. This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second...
Springer, 2016. — 352 p. Particle Systems and PDEs III, Braga, Portugal, December 2014. The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology...
Springer, 2017. — 309 p. PSPDE IV, Braga, Portugal, December 2015. "This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the...
Springer, 2007. — 343 p. Although some examples of phase portraits of quadratic systems can already be found in the work of Poincaré, the first paper dealing exclusively with these systems was published by Büchel in 1904. By the end of the 20th century an increasing flow of publications resulted in nearly a thousand papers on the subject. This book attempts to give a presentation...
Routledge, 1961. — 103 p. The book is an introduction both to Laplace's equation and its solutions and to a general method of treating partial differential equations. Chapter 1 discusses vector fields and shows how Laplace's equation arises for steady fields which are irrotational and solenoidal. In the second chapter the method of separation of variables is introduced and used to...
Springer, 1985. — 359 p. Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades...It is a superb book, which must be present in every mathematical library, and an...
Springer, 2007. — 537 p. Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades...It is a superb book, which must be present in every mathematical library, and an...
Marcel Dekker, 1999. — 308 p. Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects.
Springer, 2011. — 145 p. There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general...
Springer, 1988. — 434 p. This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
North Holland, 1988. — 242 p. The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists. The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader...
Cambridge University Press, 2008. — 233 p. This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given...
Routledge, 1964. — 74 p. The main purpose of this book is to give a thoroughly elementary account of the 'operational method' for solving linear differential equations with constant coefficients, subject to prescribed initial conditions. No previous knowledge of differential equations will be demanded from the reader, and accordingly the basic properties of linear differential...
Springer, 1969. — 154 p. The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of development and simplicity, and the operator method permits us to exploit thi s theory...
D. Van Nostrand Company , 1967. — 226 p. Too frequently, undergraduates taking courses for an honours degree in mathelnatics first encounter partial differential equations in the mathematical physics part of their curricula, when solutions to the elementary problems that occur are conjured ad hoc from nowhere, as if by magic. Thus I have found undergraduates quite surprised to...
Springer, 1996. — 440 p. Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical...
Springer, 1987. — 174 p. Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which...
World Scientific, 2000. — 224 p. The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations....
University of Oxford, 2006. — 106 p. This thesis is a model-theoretic study of exponential differential equations in the context of differential algebra. I define the theory of a set of differential equations and give an axiomatization for the theory of the exponential differential equations of split semiabelian varieties. In particular, this includes the theory of the equations...
Scittish Academic Press, 1973. — 136 p. The second-order linear ordinary differential equation with real periodic coefficients, commonly known as Hill's equation, has been investigated by many mathematicians in recent years. An account of much of this theory, in part summarized, is given in the book by Magnus and Winkler. Further results relating to eigenfunction theory are...
North Holland, 1982. — 575 p. Since the fifties, the theory of partial differential equations has undergone considerable development , yet it is certainly one of those fields where we find both the largest number of research articles and the smallest number of works of synthesis. The specialist can come to terms with such a situation, but the student who desires an introduction...
Chapman and Hall/CRC, 2005. — 417 p. The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between...