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Thursday, May 7, 2020 | History

3 edition of Theory and applications of some new classes of integral equations. found in the catalog.

Theory and applications of some new classes of integral equations.

by A. G. Ramm

  • 147 Want to read
  • 26 Currently reading

Published by Springer-Verlag in New York [etc.] .
Written in


The Physical Object
Paginationxiii, 343 p.
Number of Pages343
ID Numbers
Open LibraryOL22776047M
ISBN 100387905405

Fredholm theory. § 3. Integral equation with symmetric kernel.^ From the hypothesis K(s,t) = K(t,s) follows immediately kij = kjf, * In virtue of theo (I), any other biorthogonal system of functions satisfying (d), (e) and (/) leads to the same solutions of the integral equations as that obtained by using the. MATH - Partial Differential Equations I - 3 cr. Prerequisite: MATH and or consent of department. Basic techniques for solving linear partial differential equations, separation of variables, eigenfunction expansions, integral transforms, Sturm-Liouville boundary value problems, initial value problems and boundary value problems for hyperbolic, parabolic, and elliptic equations.

I'm looking for a good reference on integral equations (i.e., an equation in which an unknown function appears under an integral sign such as the Fredholm equation). I would like something accessible but covers approaches to showing existence. More than integral equations and their solutions are given in the first part of the book (Chapters 1–6). A lot of new e xact solutions to linear and nonlinear equations are included.

On some classes of Volterra integral equations Teresa Diogo Instituto Superior Técnico, Universidade de Lisboa E-mail: [email protected] Abstract Many physical, chemical and biological problems are modelled as nonlinear singu-lar Volterra integral equations (VIEs). One can find in the literature numerous papersFile Size: KB. This course will introduce and develop some key invariants of manifold theory and their roles in manifold classification and other applications. The invariants to be studied include some from algebraic K-theory, e.g., Whitehead torsion and Reidemeister torsion, and .


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Theory and applications of some new classes of integral equations by A. G. Ramm Download PDF EPUB FB2

This book is intended for &tudents, research engineers, and mathematicians interested in applications or numerical Theory and applications of some new classes of integral equations. book. Pure analysts will also find some new problems to tackle.

Most of the material can be understood by a reader with a relatively modest knowledge of differential and inte­ gral equations and functional analysis. This book is intended for &tudents, research engineers, and mathematicians interested in applications or numerical analysis.

Pure analysts will also find some new problems to tackle. Most of the material can be understood by a reader with a relatively modest knowledge of differential and inte­ gral. ISBN: OCLC Number: Description: xiii, pages ; 24 cm: Contents: Investigation of a new class of integral equations and applications to estimation problems (filtering, prediction, system identification) --Investigation of integral equations of the static and quasi-static fields and applications to the scattering from small bodies.

Integral equations arise in many scientific and engineering problems. A large class of initial and boundary value problems can be converted to Volterra or Fredholm integral equations.

The potential theory contributed more than any field to give rise to integral by: 4. integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems.

It also contains elegant analytical and numerical methods, and an important topic of the variational principles.

This book is primarily. This classic text on integral equations by the late Professor F. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level.

To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the 5/5(2).

Get this from a library. Integral equations and applications. [C Corduneanu] -- The purpose of this book is threefold: to be used for graduate courses on integral equations; to be a reference for researchers; and to describe methods of application of the theory. The author.

Alexander G. Ramm (born in St. Petersburg, Russia) is an American mathematician. His research focuses on differential and integral equations, operator theory, ill-posed and inverse problems, scattering theory, functional analysis, spectral theory, numerical analysis, theoretical electrical engineering, signal estimation, and tomography.

Integral Equations is quickly becoming one of the most important topics in science and engineering. This wonderful book, using an informal, conversational writing style(and at a super cheap price!) describes this immensely important area of study, without bogging down the reader in too much complicated math/5(7).

The chapter presents some applications to non-linear ordinary and partial differential equations. Some non-linear integral equations arising in science, including non-linear integral equations in neutron transport theory, nuclear physics, and infectious disease modeling have been considered.

Some results that have physical meaning have been. New to the Second Edition • New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions • More than new. Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake.

A helpful index concludes the by: The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science.

This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. From the reviews of the First Edition: "Extremely clear, self-contained text offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquées.

Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as Reviews: 2.

This chapter discusses the periodic solutions of some integral equations from the theory of epidemics. It summarizes results on an integral equation.

A key role in the abstract theory underlying these results is played by the fixed point index. The chapter presents the proof of some new results about the fixed point index of cone maps. The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

♥ Book Title: Hypersingular Integral Equations and Their Applications ♣ Name Author: I.K. Lifanov ∞ Launching: Info ISBN Link: ⊗ Detail ISBN code: ⊕ Number Pages: Total sheet ♮ News id: vEu8BmL_lWIC Download File Start Reading ☯ Full Synopsis: "A number of new methods for solving singular and hypersingular integral equations have.

MT - Integral equations Introduction Integral equations occur in a variety of applications, often being obtained from a differential equation. The reason for doing this is that it may make solution of the problem easier or, sometimes, enable us to prove fundamental results on the existence and uniqueness of.

Integral equations became the object of special attention of mathematicians after the solution of the Dirichlet problem for the Laplace equation had been reduced to the study of a linear integral equation of the second kind. The construction of a general theory of linear integral equations was begun at the end of the 19th century.

The course will cover both the basic theory of Riemann-Hilbert problems and also present some of the many applications of the theory to the analysis of integrable PDEs such as KdV and NLS, to random matrix theory, to combinatorial problems such as Ulam's increasing subsequence problem, and also to orthogonal polynomials.

In mathematics, integral equations are equations in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way.

See, for example, Green's function, Fredholm theory, and Maxwell's equations. 2 Numerical solution. 3 Classification.The Journal of Integral Equations and Applications, founded inendeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field.We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type.

Those integral equations play very significant role in applications to the description Author: Nurgali K. Ashirbayev, Józef Banaś, Raina Bekmoldayeva.