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 : 85. 71 MB
Format : PDF
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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 : 87. 24 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.

A First Course In Partial Differential Equations

Author : H. F. Weinberger
ISBN : 9780486132044
Genre : Mathematics
File Size : 31. 18 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.

Asymptotic Expansions For Ordinary Differential Equations

Author : Wolfgang Wasow
ISBN : 9780486824581
Genre : Mathematics
File Size : 77. 90 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.

Ordinary Differential Equations

Author : Morris Tenenbaum
ISBN : 9780486649405
Genre : Mathematics
File Size : 46. 10 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.

Differential Equations

Author : F.G. Tricomi
ISBN : 9780486299297
Genre : Mathematics
File Size : 20. 88 MB
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Practical, concise text covers the existence and uniqueness theorem, characteristics of first-order equations, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. 1961 edition.

Linear Differential Operators

Author : Cornelius Lanczos
ISBN : 0486680355
Genre : Mathematics
File Size : 89. 45 MB
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The basic and characteristic properties of linear differential operators are explored in this graduate-level text. No specific knowledge beyond the usual introductory courses is necessary. Includes 350 problems and solution.

Introduction To Nonlinear Differential And Integral Equations

Author : Harold Thayer Davis
ISBN : 0486609715
Genre : Mathematics
File Size : 34. 10 MB
Format : PDF, Kindle
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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.

Ordinary Differential Equations And Dynamical Systems

Author : Gerald Teschl
ISBN : 9780821883280
Genre : Mathematics
File Size : 75. 83 MB
Format : PDF
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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.

Lectures On Ordinary Differential Equations

Author : Witold Hurewicz
ISBN : 9780486797212
Genre : Mathematics
File Size : 21. 58 MB
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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.

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