ordinary differential equations in the complex domain dover books on mathematics

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Ordinary Differential Equations In The Complex Domain

Author : Einar Hille
ISBN : 0486696200
Genre : Mathematics
File Size : 83. 71 MB
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Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

Ordinary Differential Equations

Author : Edward L. Ince
ISBN : 9780486158211
Genre : Mathematics
File Size : 26. 17 MB
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Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

Asymptotic Expansions For Ordinary Differential Equations

Author : Wolfgang Wasow
ISBN : 9780486824581
Genre : Mathematics
File Size : 69. 97 MB
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This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

A First Course In Partial Differential Equations

Author : H. F. Weinberger
ISBN : 9780486132044
Genre : Mathematics
File Size : 45. 41 MB
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Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Ordinary Differential Equations

Author : Morris Tenenbaum
ISBN : 9780486649405
Genre : Mathematics
File Size : 90. 50 MB
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Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Linear Differential Equations In The Complex Domain

Author : Yasutaka Sibuya
ISBN : 9780821846766
Genre : Mathematics
File Size : 22. 59 MB
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This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.

Ordinary Differential Equations And Dynamical Systems

Author : Gerald Teschl
ISBN : 9780821883280
Genre : Mathematics
File Size : 74. 4 MB
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This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Introduction To Nonlinear Differential And Integral Equations

Author : Harold Thayer Davis
ISBN : 0486609715
Genre : Mathematics
File Size : 76. 29 MB
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Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Existence Theorems For Ordinary Differential Equations

Author : Francis J. Murray
ISBN : 9780486154954
Genre : Mathematics
File Size : 87. 43 MB
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This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.

Geometrical Methods In The Theory Of Ordinary Differential Equations

Author : V.I. Arnold
ISBN : 9781461210375
Genre : Mathematics
File Size : 70. 41 MB
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Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.

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