Partial Differential And Integral Equations
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Lectures On Differential And Integral Equations
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Author : K?saku Yoshida
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01
Lectures On Differential And Integral Equations written by K?saku Yoshida and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
Lucid, self-contained exposition of theory of ordinary differential equations and integral equations. Boundary value problem of second order linear ordinary differential equations, Fredholm integral equations, many other topics. Bibliography. 1960 edition.
Techniques Of Functional Analysis For Differential And Integral Equations
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Author : Paul Sacks
language : en
Publisher: Academic Press
Release Date : 2017-05-16
Techniques Of Functional Analysis For Differential And Integral Equations written by Paul Sacks and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Differential And Integral Equations
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Author : Peter J. Collins
language : en
Publisher: OUP Oxford
Release Date : 2006-08-03
Differential And Integral Equations written by Peter J. Collins and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Mathematics categories.
Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis. Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.
Singular Differential And Integral Equations With Applications
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-31
Singular Differential And Integral Equations With Applications written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Mathematics categories.
In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.
Partial Differential Equations Of Mathematical Physics And Integral Equations
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Author : Ronald B. Guenther
language : en
Publisher: Courier Corporation
Release Date : 1996-02-09
Partial Differential Equations Of Mathematical Physics And Integral Equations written by Ronald B. Guenther and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-09 with Mathematics categories.
Superb treatment for math and physical science students discusses modern mathematical techniques for setting up and analyzing problems. Discusses partial differential equations of the 1st order, elementary modeling, potential theory, parabolic equations, more. 1988 edition.
Analysis Of Approximation Methods For Differential And Integral Equations
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Author : Hans-Jürgen Reinhardt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Approximation Methods For Differential And Integral Equations written by Hans-Jürgen Reinhardt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.
Partial Differential Equations
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Author : Friedrich Sauvigny
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-04
Partial Differential Equations written by Friedrich Sauvigny and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-04 with Mathematics categories.
This comprehensive two-volume textbook covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is placed on the connection of PDEs and complex variable methods. In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. We solve partial differential equations via integral representations in this volume, reserving functional analytic solution methods for Volume Two.
Integral Equations
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Author : Wolfgang Hackbusch
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Integral Equations written by Wolfgang Hackbusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Differential And Integral Equations Through Practical Problems And Exercises
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Author : G. Micula
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Differential And Integral Equations Through Practical Problems And Exercises written by G. Micula and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Many important phenomena are described and modeled by means of differential and integral equations. To understand these phenomena necessarily implies being able to solve the differential and integral equations that model them. Such equations, and the development of techniques for solving them, have always held a privileged place in the mathematical sciences. Today, theoretical advances have led to more abstract and comprehensive theories which are increasingly more complex in their mathematical concepts. Theoretical investigations along these lines have led to even more abstract and comprehensive theories, and to increasingly complex mathematical concepts. Long-standing teaching practice has, however, shown that the theory of differential and integral equations cannot be studied thoroughly and understood by mere contemplation. This can only be achieved by acquiring the necessary techniques; and the best way to achieve this is by working through as many different exercises as possible. The eight chapters of this book contain a large number of problems and exercises, selected on the basis of long experience in teaching students, which together with the author's original problems cover the whole range of current methods employed in solving the integral, differential equations, and the partial differential equations of order one, without, however, renouncing the classical problems. Every chapter of this book begins with the succinct theoretical exposition of the minimum of knowledge required to solve the problems and exercises therein.
Partial Differential And Integral Equations
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Author : Heinrich Begehr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Partial Differential And Integral Equations written by Heinrich Begehr and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.