Author: Horace Perry Flatt
Publisher:
ISBN:
Category :
Languages : en
Pages : 65

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Book Description

Author: Laszlo Szekelyhidi
Publisher: World Scientific Publishing Company
ISBN: 9814725013
Category : Mathematics
Languages : en
Pages : 254

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Book Description
This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations.In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

Author: Charles Henry Edwards
Publisher:
ISBN: 9780138141028
Category : Algebras, Linear
Languages : en
Pages : 762

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Book Description
For courses in Differential Equations and Linear Algebra. Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed-yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.

Author: Richard S. Palais
Publisher: American Mathematical Soc.
ISBN: 0821821385
Category : Mathematics
Languages : en
Pages : 329

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Book Description
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486318265
Category : Mathematics
Languages : en
Pages : 369

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Book Description
With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Author: Frank Stenger
Publisher: Springer
ISBN: 3319275267
Category : Mathematics
Languages : en
Pages : 232

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Book Description
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ R3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ R3 × [0, T], and provide an explicit novel algorithm based on Sinc approximation and Picard–like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions.

Author: I. M. Gel'fand
Publisher: Academic Press
ISBN: 1483262324
Category : Mathematics
Languages : en
Pages : 233

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Book Description
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.

Author: Ravi P Agarwal
Publisher: World Scientific Publishing Company
ISBN: 9813104619
Category : Mathematics
Languages : en
Pages : 332

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Book Description
This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

Author: Carmen Chicone
Publisher: Springer Science & Business Media
ISBN: 0387357947
Category : Mathematics
Languages : en
Pages : 652

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Book Description
Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Author: John M. Rassias
Publisher: World Scientific
ISBN: 9789810204617
Category : Mathematics
Languages : en
Pages : 198

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Book Description
Based on a semester course taught in Greece for many years to science, engineering, and mathematics students. Discusses continuity and linearity, differentiability and analyticity, extrema, existence, uniqueness, stability, and other topics. The examples are drawn from the literature of the field. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR