Advanced Differential Equations
Advanced Differential Equations

Author: M.D.Raisinghania

Publisher: S. Chand Publishing

Published: 1995-03

Total Pages: 1366

ISBN-13: 8121908930

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This book is especially prepared for B.A., B.Sc. and honours (Mathematics and Physics), M.A/M.Sc. (Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., AMIE, GATE, and other competitve exams.Almost all the chapters have been rewritten so that in the present form, the reader will not find any difficulty in understanding the subject matter.The matter of the previous edition has been re-organised so that now each topic gets its proper place in the book.More solved examples have been added so that now each topic gets its proper place in the book. References to the latest papers of various universities and I.A.S. examination have been made at proper places.

ADVANCED DIFFERENTIAL EQUATIONS
ADVANCED DIFFERENTIAL EQUATIONS

Author: M D RAISINGHANIA

Publisher: S. Chand Publishing

Published: 2018

Total Pages:

ISBN-13: 9352535898

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This book has been designed to acquaint the students with advanced concepts of differential equations. Comprehensively written, it covers topics such as Boundary Value Problems and their Separation of Variables, Laplace Transforms with Applications, Fourier Transforms and their Applications, the Hankel Transform and its Applications and Calculus of Variations. While the textbook lucidly explains the theoretical concepts, it also presents the various methods and applications related to differential equations. Students of mathematics would find this book extremely useful as well as the aspirants of various competitive examinations.

Advanced Differential Equations, 20e
Advanced Differential Equations, 20e

Author: Raisinghania M.D.

Publisher: S. Chand Publishing

Published:

Total Pages: 1084

ISBN-13: 9355014678

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This book is especially written for the students of B.A. (Mathematics), B.Sc., (Mathematics & Physics), M.A. (Mathematics), M.Sc. (Mathematics & Physics) and B.E./B.Tech. Besides, it will also be of immense value to the aspirants of AMIE,GATE, CSIR- UGC (NET) and other competitive examinations. A set of objective problems (including questions asked in the examinations of various universities, GATE, NET, etc.) has been provided at the end of each chapter. Also, several new solved examples have been added so that the reader may gain confidence in the techniques of solving problems.

A Second Course in Elementary Differential Equations
A Second Course in Elementary Differential Equations

Author: Paul Waltman

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 272

ISBN-13: 1483276600

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A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.

Partial Differential Equations and Complex Analysis
Partial Differential Equations and Complex Analysis

Author: Steven G. Krantz

Publisher: CRC Press

Published: 1992-07-02

Total Pages: 322

ISBN-13: 9780849371554

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Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

Advanced Numerical Methods for Differential Equations
Advanced Numerical Methods for Differential Equations

Author: Harendra Singh

Publisher: CRC Press

Published: 2021-07-29

Total Pages: 337

ISBN-13: 1000381080

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Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Introduction to Ordinary Differential Equations
Introduction to Ordinary Differential Equations

Author: Albert L. Rabenstein

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 444

ISBN-13: 1483226220

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Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.

Fourier Analysis and Partial Differential Equations
Fourier Analysis and Partial Differential Equations

Author: Iorio Júnior Iorio Jr.

Publisher: Cambridge University Press

Published: 2001-03-15

Total Pages: 428

ISBN-13: 9780521621168

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This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.

Differential Equations, Stability, and Chaos in Dynamic Economics
Differential Equations, Stability, and Chaos in Dynamic Economics

Author: William A. Brock

Publisher: North Holland

Published: 1989

Total Pages: 414

ISBN-13:

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This is the first economics work of its kind offering the economist the opportunity to acquire new and important analytical tools. It introduces the reader to three advanced mathematical methods by presenting both their theoretical bases and their applications to a wide range of economic models. The mathematical methods presented are ordinary differential equations, stability techniques and chaotic dynamics. Topics such as existence, continuation of solutions, uniqueness, dependence on initial data and parameters, linear systems, stability of linear systems, two dimensional phase analysis, local and global stability, the stability manifold, stability of optimal control and empirical tests for chaotic dynamics are covered and their use in economic theory is illustrated in numerous applications. These applications include microeconomic dynamics, investment theory, macroeconomic policies, capital theory, business cycles, financial economics and many others. All chapters conclude with two sections on miscellaneous applications and exercises and further remarks and references. In total the reader will find a valuable guide to over 500 selected references that use differential equations, stability analysis and chaotic dynamics. Graduate students in economics with a special interest in economic theory, economic researchers and applied mathematicians will all benefit from this volume.