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Lectures on the Theory of Group Properties of Differential Equations

Lectures on the Theory of Group Properties of Differential Equations Author L V Ovsyannikov
ISBN-10 9789814460835
Release 2013-05-20
Pages 156
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These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models.



Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations Author Peter J. Olver
ISBN-10 0387950001
Release 2000-01-21
Pages 513
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This is a solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasizing explicit examples and computations. Further examples and new theoretical developments appear in the exercises at the end of each chapter.



Group Properties Of The Acoustic Differential Equation

Group Properties Of The Acoustic Differential Equation Author L V Poluyanov
ISBN-10 9781482272659
Release 2014-04-21
Pages 166
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This text is an addition to the existing literature about the symmetrical properties of sound waves. The authors clarify the algebraic and analytical nature of the dynamic acoustic problem. Operator equations which are typical for linear systems and the more general Lie method are considered, which can be applied even to nonlinear problems. The information obtained allows the reader to construct different types of analytical solutions of the different acoustic equation. The acoustic differential equation describes sound waves in elastic media. If the media is non-homogeneous then the acoustic equation is generally very complicated and its exact solutions or analytical solutions may be considered as rare. This volume applies Lie algebra and Lie group techniques to separate independent variables and obtains exact analytical solutions. Special attention is paid to homogeneous and non-homogeneous media with different symmetry properties. The full wave acoustic equation is considered as well as the so-called phase acoustic equation which arises in the short-wave approximation.



Lectures on Ordinary Differential Equations

Lectures on Ordinary Differential Equations Author Witold Hurewicz
ISBN-10 9780486797212
Release 2014-07-21
Pages 144
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Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.



Geometrical Properties of Differential Equations

Geometrical Properties of Differential Equations Author Ljudmila A Bordag
ISBN-10 9789814667265
Release 2015-05-27
Pages 340
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This textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics. We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way. The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study. The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).



Lectures on Analytic Differential Equations

Lectures on Analytic Differential Equations Author I͡U. S. Ilʹi͡ashenko
ISBN-10 9780821836675
Release 2008
Pages 625
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The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text. The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.



Lectures on Analytic Differential Equations

Lectures on Analytic Differential Equations Author I͡U. S. Ilʹi͡ashenko
ISBN-10 0821872486
Release
Pages 625
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Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text." "The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area."--BOOK JACKET.



Equadiff 7 Partial differential equations Numerical methods applications

Equadiff 7    Partial differential equations  Numerical methods   applications Author
ISBN-10 UOM:39015019565848
Release 1989
Pages
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Equadiff 7 Partial differential equations Numerical methods applications has been writing in one form or another for most of life. You can find so many inspiration from Equadiff 7 Partial differential equations Numerical methods applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Equadiff 7 Partial differential equations Numerical methods applications book for free.



Linear Differential Equations and Group Theory from Riemann to Poincare

Linear Differential Equations and Group Theory from Riemann to Poincare Author Jeremy Gray
ISBN-10 0817647724
Release 2008-01-21
Pages 338
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This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.



Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations Author Matthew Witten
ISBN-10 9781483151359
Release 2014-05-23
Pages 268
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Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic McKendrick equations for age-structured population growth; and logistic models of structured population growth. A number of book reviews are also included. This journal provides an interdisciplinary forum for the presentation of results not included in other particular journals, and thus will be beneficial to those interested in this field of study.



Lectures on p adic Differential Equations

Lectures on p adic Differential Equations Author Bernard Dwork
ISBN-10 9781461381938
Release 2012-12-06
Pages 310
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The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... .



Automated Solution of Differential Equations by the Finite Element Method

Automated Solution of Differential Equations by the Finite Element Method Author Anders Logg
ISBN-10 9783642230998
Release 2012-02-24
Pages 731
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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.



Lectures on mixed problems in partial differential equations and representation of semi groups

Lectures on mixed problems in partial differential equations and representation of semi groups Author Laurent Schwartz
ISBN-10 UOM:39015017420509
Release 1957
Pages 236
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Lectures on mixed problems in partial differential equations and representation of semi groups has been writing in one form or another for most of life. You can find so many inspiration from Lectures on mixed problems in partial differential equations and representation of semi groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Lectures on mixed problems in partial differential equations and representation of semi groups book for free.



Lectures Problems And Solutions For Ordinary Differential Equations Second Edition

Lectures  Problems And Solutions For Ordinary Differential Equations  Second Edition Author Deng Yuefan
ISBN-10 9789813226159
Release 2017-08-11
Pages 572
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Lectures Problems And Solutions For Ordinary Differential Equations Second Edition has been writing in one form or another for most of life. You can find so many inspiration from Lectures Problems And Solutions For Ordinary Differential Equations Second Edition also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Lectures Problems And Solutions For Ordinary Differential Equations Second Edition book for free.



Proceedings of the Conference on Differential Equations and the Stokes Phenomenon

Proceedings of the Conference on Differential Equations and the Stokes Phenomenon Author Boele Lieuwe Jan Braaksma
ISBN-10 9812381724
Release 2002
Pages 329
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Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.



The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations Author Kai Diethelm
ISBN-10 9783642145742
Release 2010-08-18
Pages 247
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Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.



Lectures on Algebra

Lectures on Algebra Author Shreeram Shankar Abhyankar
ISBN-10 9789812568267
Release 2006
Pages 746
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This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.