Theory Of Third Order Differential Equations

Author : Seshadev Padhi,Smita Pati
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 48,9 Mb
Release : 2013-10-16
Category : Mathematics
ISBN : 9788132216148

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Theory of Third-Order Differential Equations by Seshadev Padhi,Smita Pati Pdf

This book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained. Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-order linear differential equations with constant coefficients, and a brief introduction to delay differential equations is given. The oscillation and asymptotic behavior of non-oscillatory solutions of homogeneous third-order linear differential equations with variable coefficients are discussed in Ch. 2. The results are extended to third-order linear non-homogeneous equations in Ch. 3, while Ch. 4 explains the oscillation and non-oscillation results for homogeneous third-order nonlinear differential equations. Chapter 5 deals with the z-type oscillation and non-oscillation of third-order nonlinear and non-homogeneous differential equations. Chapter 6 is devoted to the study of third-order delay differential equations. Chapter 7 explains the stability of solutions of third-order equations. Some knowledge of differential equations, analysis and algebra is desirable, but not essential, in order to study the topic.

Author : Michal Gregus
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400937154

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Third Order Linear Differential Equations by Michal Gregus Pdf

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Gad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. How ever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the stI11fture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci plines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifi~ation schemes.

Author : Jane Cronin
Publisher : CRC Press
Page : 408 pages
File Size : 42,6 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9781420014938

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Ordinary Differential Equations by Jane Cronin Pdf

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of

Author : Joseph Grifone,Zoltán Muzsnay
Publisher : World Scientific
Page : 228 pages
File Size : 55,6 Mb
Release : 2000-05-25
Category : Mathematics
ISBN : 9789814495363

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Variational Principles for Second-Order Differential Equations by Joseph Grifone,Zoltán Muzsnay Pdf

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. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi–Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer–Quillen–Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. Contents:An Introduction to Formal Integrability Theory of Partial Differential SystemsFrölicher–Nijenhuis Theory of DerivationsDifferential Algebraic Formalism of ConnectionsNecessary Conditions for Variational SpraysObstructions to the Integrability of the Euler–Lagrange SystemThe Classification of Locally Variational Sprays on Two-Dimensional ManifoldsEuler–Lagrange Systems in the Isotropic Case Readership: Mathematicians. Keywords:Calculus of Variations;Inverse Problem;Euler-Lagrange Equation;Sprays;Formal Integrability;Involution;Janet-Riquier Theory;Spencer TheoryReviews: “Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should take a look at this book.” Zentralblatt MATH

Author : Po-Fang Hsieh,Yasutaka Sibuya
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215066

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Basic Theory of Ordinary Differential Equations by Po-Fang Hsieh,Yasutaka Sibuya Pdf

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.

Author : Michael Ruzhansky,Jens Wirth
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 46,8 Mb
Release : 2011-05-04
Category : Mathematics
ISBN : 9783034800693

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Modern Aspects of the Theory of Partial Differential Equations by Michael Ruzhansky,Jens Wirth Pdf

The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

Author : Vladimir Kozlov,Vladimir Maz'ya
Publisher : Springer
Page : 148 pages
File Size : 49,5 Mb
Release : 2006-11-13
Category : Mathematics
ISBN : 9783540691228

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Theory of a Higher-Order Sturm-Liouville Equation by Vladimir Kozlov,Vladimir Maz'ya Pdf

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Author : Fritz Schwarz
Publisher : CRC Press
Page : 448 pages
File Size : 45,7 Mb
Release : 2007-10-02
Category : Mathematics
ISBN : 1584888903

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Algorithmic Lie Theory for Solving Ordinary Differential Equations by Fritz Schwarz Pdf

Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble

Author : Ti-Jun Xiao,Jin Liang
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 54,6 Mb
Release : 1998-11-18
Category : Mathematics
ISBN : 3540652388

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The Cauchy Problem for Higher Order Abstract Differential Equations by Ti-Jun Xiao,Jin Liang Pdf

This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.

Author : Luis Manuel Braga da Costa Campos
Publisher : CRC Press
Page : 394 pages
File Size : 51,6 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9780429644177

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Higher-Order Differential Equations and Elasticity by Luis Manuel Braga da Costa Campos Pdf

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 set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic. Discusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves Presents differential equations of the second and higher order, including non-linear and with variable coefficients Compares relation of differentials with the principles of thermodynamics Describes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates Presents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates

Author : Ravi P Agarwal
Publisher : World Scientific
Page : 321 pages
File Size : 42,6 Mb
Release : 1986-07-01
Category : Mathematics
ISBN : 9789814513630

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Boundary Value Problems From Higher Order Differential Equations by Ravi P Agarwal Pdf

Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems

Author : Andrew Russell Forsyth
Publisher : CUP Archive
Page : 620 pages
File Size : 55,8 Mb
Release : 1959
Category : Differential equations
ISBN : 8210379456XXX

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Theory of Differential Equations by Andrew Russell Forsyth Pdf

Author : Kam Tim Chau
Publisher : CRC Press
Page : 1399 pages
File Size : 51,8 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9781351675628

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Theory of Differential Equations in Engineering and Mechanics by Kam Tim Chau Pdf

This gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications. This first volume covers a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus more advanced topics such as Green’s function method, integral and integro-differential equations, asymptotic expansion and perturbation, calculus of variations, variational and related methods, finite difference and numerical methods. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in these books providing valuable information and mathematics background for their multi-disciplinary research and education.

Author : W. R. Utz
Publisher : Unknown
Page : 16 pages
File Size : 54,9 Mb
Release : 1955
Category : Differential equations, Linear
ISBN : UOM:39015095244243

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A Third Order Differential Equation by W. R. Utz Pdf

Author : Steven G. Krantz
Publisher : Unknown
Page : 0 pages
File Size : 51,9 Mb
Release : 2022
Category : Electronic
ISBN : 1032102713

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Differential Equations by Steven G. Krantz Pdf

Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Author -- 1. What is a Differential Equation? -- 1.1. Introductory Remarks -- 1.2. A Taste of Ordinary Differential Equations -- 1.3. The Nature of Solutions -- 2. Solving First-Order Equations -- 2.1. Separable Equations -- 2.2. First-Order Linear Equations -- 2.3. Exact Equations -- 2.4. Orthogonal Trajectories and Families -- 2.5. Homogeneous Equations -- 2.6. Integrating Factors -- 2.7. Reduction of Order -- 2.7.1. Dependent Variable Missing -- 2.7.2. Independent Variable Missing -- 3. Some Applications of the First-Order Theory -- 3.1. The Hanging Chain and Pursuit Curves -- 3.1.1. The Hanging Chain -- 3.1.2. Pursuit Curves -- 3.2. Electrical Circuits -- 4. Second-Order Linear Equations -- 4.1. Second-Order Linear Equations with Constant Coefficients -- 4.2. The Method of Undetermined Coefficients -- 4.3. The Method of Variation of Parameters -- 4.4. The Use of a Known Solution to Find Another -- 4.5. Higher-Order Equations -- 5. Applications of the Second-Order Theory -- 5.1. Vibrations and Oscillations -- 5.1.1. Undamped Simple Harmonic Motion -- 5.1.2. Damped Vibrations -- 5.1.3. Forced Vibrations -- 5.1.4. A Few Remarks about Electricity -- 5.2. Newton's Law of Gravitation and Kepler's Laws -- 5.2.1. Kepler's Second Law -- 5.2.2. Kepler's First Law -- 5.2.3. Kepler's Third Law -- 6. Power Series Solutions and Special Functions -- 6.1. Introduction and Review of Power Series -- 6.1.1. Review of Power Series -- 6.2. Series Solutions of First-Order Equations -- 6.3. Ordinary Points -- 6.4. Regular Singular Points -- 6.5. More on Regular Singular Points -- 7. Fourier Series: Basic Concepts -- 7.1. Fourier Coefficients -- 7.2. Some Remarks about Convergence -- 7.3. Even and Odd Functions: Cosine and Sine Series.