Ordinary Differential Equations in the Complex Domain


Author: Einar Hille
Publisher: Courier Corporation
ISBN: 9780486696201
Category: Mathematics
Page: 484
View: 1734

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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.

Linear Differential Equations in the Complex Domain

Problems of Analytic Continuation
Author: Yasutaka Sibuya
Publisher: American Mathematical Soc.
ISBN: 0821846760
Category: Mathematics
Page: 267
View: 4770

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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


Author: Edward L. Ince
Publisher: Courier Corporation
ISBN: 0486158217
Category: Mathematics
Page: 576
View: 8809

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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
Publisher: Courier Dover Publications
ISBN: 0486824586
Category: Mathematics
Page: 384
View: 9833

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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

with Complex Variables and Transform Methods
Author: H. F. Weinberger
Publisher: Courier Corporation
ISBN: 0486132048
Category: Mathematics
Page: 480
View: 7623

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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.

Elementary Functional Analysis


Author: Georgi E. Shilov
Publisher: Courier Corporation
ISBN: 0486318680
Category: Mathematics
Page: 352
View: 9229

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Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.

Lectures on Ordinary Differential Equations


Author: Witold Hurewicz
Publisher: Courier Corporation
ISBN: 9780486495101
Category: Mathematics
Page: 144
View: 6536

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"A rigorous and lively introduction . . . careful and lucid . . ."--The American Mathematical Monthly. Excellent hardcover edition. This concise and idea-rich introduction to a topic of perennial interest in mathematics is written so clearly and lucidly, it is well within the reach of senior mathematics students. It covers mainly existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Throughout, the emphasis is on geometric methods. Witold Hurewicz was a world-class mathematician whose untimely death in 1956 deprived the mathematics community of one of its leading lights. His contributions to dimension theory, homotopy and other topics are outlined by Professor Solomon Lefschetz in a prefatory article "Witold Hurewicz in Memoriam" included in this volume. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works. Unabridged Dover republication of the work originally published by MIT Press, 1958. Prefatory article "Witold Hurewicz in Memoriam" by Solomon Lefschetz. List of References. Index. 26 figures.

Ordinary Differential Equations


Author: Morris Tenenbaum,Harry Pollard
Publisher: Courier Corporation
ISBN: 9780486134642
Category: Mathematics
Page: 818
View: 2105

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This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences. The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations. The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.

Modern Nonlinear Equations


Author: Thomas L. Saaty
Publisher: Courier Corporation
ISBN: 0486143767
Category: Mathematics
Page: 496
View: 6668

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Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." — Math Reviews. 1964 edition.

Linear Differential Operators


Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 9780486680354
Category: Mathematics
Page: 564
View: 8939

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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.

Differential Equations


Author: F. G. Tricomi,Elizabeth A. McHarg
Publisher: Courier Corporation
ISBN: 0486488195
Category: Mathematics
Page: 273
View: 8244

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This practical, concise teaching text by a noted educator covers the essential background for advanced courses in mathematical analysis. Topics include the existence and uniqueness theorem, behavior of characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. 1961 edition.

Advanced engineering mathematics


Author: Erwin Kreyszig
Publisher: John Wiley & Sons
ISBN: N.A
Category: Mathematics
Page: 1294
View: 8063

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This market leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises and self contained subject matter parts for maximum flexibility. Thoroughly updated and streamlined to reflect new developments in the field, the ninth edition of this bestselling text features modern engineering applications and the uses of technology. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector Calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; and Probability and Statistics.

The Skeleton Key of Mathematics

A Simple Account of Complex Algebraic Theories
Author: Dudley Ernest Littlewood
Publisher: Courier Corporation
ISBN: 9780486425436
Category: Mathematics
Page: 138
View: 6640

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As the title promises, this helpful volume offers easy access to the abstract principles common to science and mathematics. It eschews technical terms and omits troublesome details in favor of straightforward explanations that will allow scientists to read papers in branches of science other than their own, mathematicians to appreciate papers on topics on which they have no specialized knowledge, and other readers to cultivate an improved understanding of subjects employing mathematical principles. The broad scope of topics encompasses Euclid’s algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; the Galois theory of equations; algebraic geometry; matrices and determinants; invariants and tensors; algebras; group algebras; and more. "It is refreshing to find a book which deals briefly but competently with a variety of concatenated algebraic topics, that is not written for the specialist," enthused the Journal of the Institute of Actuaries Students’ Society about this volume, adding "Littlewood’s book can be unreservedly recommended."