Ordinary Differential Equations in the Complex Domain

Author: Einar Hille

Publisher: Courier Corporation

ISBN: 9780486696201

Category: Mathematics

Page: 484

View: 3601

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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.
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Ordinary Differential Equations

Author: Edward L. Ince

Publisher: Courier Corporation

ISBN: 0486158217

Category: Mathematics

Page: 576

View: 2614

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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.
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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: 4824

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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.
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Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Dover Publications

ISBN: 0486824586

Category: Mathematics

Page: 384

View: 5196

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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.
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Ordinary Differential Equations

Author: Morris Tenenbaum,Harry Pollard

Publisher: Courier Corporation

ISBN: 9780486134642

Category: Mathematics

Page: 818

View: 2454

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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.
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Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 1470411008

Category: Mathematical analysis

Page: 641

View: 9779

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A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
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Elementary Functional Analysis

Author: Georgi E. Shilov

Publisher: Courier Corporation

ISBN: 0486318680

Category: Mathematics

Page: 352

View: 3468

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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.
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A Course in Mathematical Analysis Volume 3

Variation of Solutions; Partial Differential Equations of the Second Order; Integral Equations; Calculus of Variations

Author: Edouard Goursat,Howard G. Bergmann

Publisher: Courier Corporation

ISBN: 0486446522

Category: Mathematics

Page: 752

View: 9843

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Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.
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Function Theory on Planar Domains

A Second Course in Complex Analysis

Author: Stephen D. Fisher

Publisher: Courier Corporation

ISBN: 0486151107

Category: Mathematics

Page: 288

View: 6442

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This treatment of complex analysis focuses on function theory on a finitely connected planar domain. It emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. 1983 edition.
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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: 4298

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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.
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