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Books on the topic 'Integral equation theories'

Author: Grafiati

Published: 7 December 2024

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1

Puoskari, Mauri. Integral equation theories of simple classical and bose liquids. Oulu, Finland: Computer Services Center and Division of Theoretical Physics, Department of Physical Sciences, University of Oulu, 1997.

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2

O'Regan, Donal. Existence theory for nonlinear integral and integrodifferential equations. Dordrecht: Kluwer Academic Press, 1998.

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3

Hackbusch, W. Integralgleichungen: Theorie und Numerik. Stuttgart: B.G. Teubner, 1989.

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4

Pipkin, A. C. A course on integral equations. New York: Springer-Verlag, 1991.

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5

Pipkin, A. C. A course on integral equations. New York: Springer-Verlag, 1991.

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6

Carmona, R. Nonlinear stochastic integrators, equations, and flows. New York: Gordon and Breach Science Publishers, 1990.

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7

Askhabov, S. N. Singuli︠a︡rnye integralʹnye uravnenii︠a︡ i uravnenii︠a︡ tipa svertki s monotonnoĭ nelineĭnostʹi︠u︡: Monografii︠a︡. Maĭkop: Izd-vo MGTU, 2004.

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8

Xing-Chang, Song, ed. Integrable systems. Singapore: World Scientific, 1990.

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9

Ibort, L. A. Integrable Systems, Quantum Groups, and Quantum Field Theories. Dordrecht: Springer Netherlands, 1993.

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10

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

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The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existence and uniqueness of such solutions. The spectral criteria for boundedness of solutions of operator equations and, as a consequence, sufficient spectral features boundedness of solutions of differential and differential-difference equations in Banach space. The results obtained for operator equations with operators and work of Volterra operators, allowed to extend to some systems of partial differential equations known spectral stability criteria for solutions of A. M. Lyapunov and also to generalize theorems on the exponential characteristic. The results of the monograph may be useful in the study of linear mechanical and electrical systems, in problems of diffraction of electromagnetic waves, theory of automatic control, etc. It is intended for researchers, graduate students functional analysis and its applications to operator and differential equations.

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11

A, Pennline James, and NASA Glenn Research Center, eds. Improving the accuracy of quadrature method solutions of Fredholm integral equations that arise from nonlinear two-point boundary value problems. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 1999.

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12

1956-, Norvaiša Rimas, ed. Concrete functional calculus. New York: Springer, 2011.

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13

Pavel, Winternitz, ed. Systèmes dynamiques non linéaires: Intégrabilité et comportement qualitatif. Montréal: Presses de l'Université de Montréal, 1986.

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14

1946-, Kupershmidt Boris A., ed. Integrable and superintegrable systems. Singapore: World Scientific, 1990.

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15

Morino, Luigi. IABEM Symposium on Boundary Integral Methods for Nonlinear Problems: Proceedings of the IABEM Symposium held in Pontignano, Italy, May 28-June 3 1995. Dordrecht: Springer Netherlands, 1997.

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16

Z, Horváth, and Palla L, eds. Conformal field theories and integrable models: Lectures held at the Eötvös Graduate course, Budapest, Hungary 13-18 August 1996. Berlin: Springer, 1997.

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17

Sabelʹfelʹd, K. K. Spherical means for PDEs. Utrecht, Netherlands: VSP, 1997.

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18

L, Leach P. G., and Steeb W. -H, eds. Proceedings of the Workshop on Finite Dimensional Integrable Nonlinear Dynamical Systems: Johannesburg, South Africa, 11-15 January 1988. Singapore: World Scientific, 1988.

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19

1980-, Moradifam Amir, ed. Functional inequalities: New perspectives and new applications. Providence, Rhode Island: American Mathematical Society, 2013.

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20

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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21

Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. Providence, Rhode Island: American Mathematical Society, 2016.

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22

Jakobson, Dmitry, Pierre Albin, and Frédéric Rochon. Geometric and spectral analysis. Providence, Rhode Island: American Mathematical Society, 2014.

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23

Mann, Peter. Vector Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0034.

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This chapter gives a non-technical overview of differential equations from across mathematical physics, with particular attention to those used in the book. It is a common trend in physics and nature, or perhaps just the way numbers and calculus come together, that, to describe the evolution of things, most theories use a differential equation of low order. This chapter is useful for those with no prior knowledge of the differential equations and explains the concepts required for a basic exposition of classical mechanics. It discusses separable differential equations, boundary conditions and initial value problems, as well as particular solutions, complete solutions, series solutions and general solutions. It also discusses the Cauchy–Lipschitz theorem, flow and the Fourier method, as well as first integrals, complete integrals and integral curves.

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24

Mann, Peter. Canonical & Gauge Transformations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0018.

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In this chapter, the Hamilton–Jacobi formulation is discussed in two parts: from a generating function perspective and as a variational principle. The Poincaré–Cartan 1-form is derived and solutions to the Hamilton–Jacobi equations are discussed. The canonical action is examined in a fashion similar to that used for analysis in previous chapters. The Hamilton–Jacobi equation is then shown to parallel the eikonal equation of wave mechanics. The chapter discusses Hamilton’s principal function, the time-independent Hamilton–Jacobi equation, Hamilton’s characteristic function, the rectification theorem, the Maupertius action principle and the Hamilton–Jacobi variational problem. The chapter also discusses integral surfaces, complete integral hypersurfaces, completely separable solutions, the Arnold–Liouville integrability theorem, general integrals, the Cauchy problem and de Broglie–Bohm mechanics. In addition, an interdisciplinary example of medical imaging is detailed.

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25

Georgiev, Svetlin G., and Inci M. Erhan. Nonlinear Integral Equations on Time Scales. Nova Science Publishers, Incorporated, 2019.

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26

Schaefer, Helmut. Neue Existenzsätze in der Theorie Nichtlinearer Integralgleichungen. de Gruyter GmbH, Walter, 2022.

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27

Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. Leipzig: B.G. Teubner, 1993.

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28

Über freie und erzwungene schwingungen: Eine einführung in die theorie der linearen integralgleichungen. Leipzig: B.G. Teubner, 1991.

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29

Schwimmer, A., L. Girardello, M. Martellini, L. Bonora, and Giuseppe Mussardo. Integrable Quantum Field Theories. Springer, 2013.

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30

Horvath, Zalan. Conformal Field Theories and Integrable Models. Springer, 2013.

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31

Morawetz, Klaus. Nonlocal Collision Integral. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0013.

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The kinetic equation with the nonlocal shifts is presented as the final result on the way to derive the kinetic equation with nonlocal corrections. The exclusive dependence of the nonlocal and non-instant corrections on the scattering phase shift confirms the results from the theory of gases. With the approximation on the level of the Brueckner reaction matrix, the corresponding non-instant and nonlocal scattering integral in parallel with the classical Enskog’s equation, can be treated with Monte-Carlo simulation techniques. Neglecting the shifts, the Landau theory of quasiparticle transport appears. In this sense the presented kinetic theory unifies both approaches. An intrinsic symmetry is found from the optical theorem which allows for representing the collision integral equivalently either in particle-hole symmetric or space-time symmetric form.

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32

Silbermann, Bernd, Steffen Roch, and Pedro A. Santos. Non-commutative Gelfand Theories. Springer, 2011.

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33

Integrable Systems. World Scientific Publishing Co Pte Ltd, 1989.

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34

Integrable Quantum Field Theories and Their Applications. World Scientific Publishing Company, 2002.

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35

Ahn, Changrim, Chaiho Rim, and Ryu Sasaki. Integrable Quantum Field Theories and Their Applications: Proceedings of the Apctp Winter School. World Scientific Publishing Co Pte Ltd, 2001.

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36

Ahn, Changrim, Chaiho Rim, and Ryu Sasaki. Integrable Quantum Field Theories and Their Applications: Proceedings of the APCTP Winter School. World Scientific Publishing Co Pte Ltd, 2001.

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37

Chang, Tai-Ping. Seismic response analysis of nonlinear structures using the stochastic equivalent linearization technique. 1985.

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38

Street, Brian. Multi-parameter Singular Integrals. (AM-189). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.001.0001.

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This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.

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39

Norvaisa, R., and R. M. Dudley. Concrete Functional Calculus. Springer, 2010.

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40

O'Regan, Donal. Existence Theory for Nonlinear Ordinary Differential Equations. Springer, 2013.

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41

O'Regan, Donal. Existence Theory for Nonlinear Ordinary Differential Equations. Springer Netherlands, 2009.

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42

Suris, Yuri B. Problem of Integrable Discretization: Hamiltonian Approach. Springer Basel AG, 2012.

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43

Non-Commutative Gelfand Theories: A Tool-Kit for Operator Theorists and Numerical Analysts. Springer London, Limited, 2010.

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44

McMaster, Brian, and Aisling McCluskey. Integration with Complex Numbers. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192846075.001.0001.

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This introductory text on complex analysis focuses on how to evaluate challenging improper (real) integrals, or their Cauchy principal values if need be, by associating them with (complex) contour integrals. On the way to this goal it explains in detail the basic arithmetic, algebra and analysis of complex numbers and functions: particularly the Cauchy–Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, Taylor’s theorem, Laurent’s theorem and Cauchy’s residue theorem. Recognising that many non-specialist cohorts need to acquire skill and confidence in these techniques, great care is taken to allow time for consolidation of fundamental ideas before proceeding to more sophisticated ones, and stress is laid on worked examples to explain ideas and applications, informal diagrams to build insight, roughwork initial explorations to help seek out solution strategies and—above all—suites of exercises in which the learner can develop and reinforce competence: learning through doing being the hallmark of the working textbook. Substantial revision sections on real analysis and calculus are built into the text for learners who may require additional preparation. An appended final chapter addresses some more advanced topics, such as uniform convergence, that are relevant to why certain key theorems work. Specimen solutions for many exercises will be made available to instructors upon application to the publishers.

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45

Mann, Peter. Differential Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0035.

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This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approach to explain how the Euler–Lagrange equation is derived using this method. It also discusses first integrals. The chapter closes by defining the functional derivative, which is used in classical field theory.

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46

Conformal Field Theories and Integrable Models: Lectures Held at the Eotvos Graduate Course, Budapest, Hungary, 13-18 August 1996 (Lecture Notes in Physics). Springer, 1997.

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47

Sulem, Catherine, Pierre Lochak, and Mikhael Balabane. Integrable Systems and Applications: Proceedings of a Workshop Held at Oléron, France, June 20-24 1988. Springer, 2014.

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48

Important developments in soliton theory. Berlin: Springer, 1993.

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49

Mann, Peter. Hamilton’s Equations & Routhian Reduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0016.

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In this chapter, the Poisson bracket and angular momentum are investigated and first integrals are used to develop conservation laws as a canonical Noether’s theorem. The Poisson bracket was developed by the French mathematician Poisson in the late nineteenth century and it is a reformulation, or at least a tidying up, of Hamilton’s equations into one neat package. The Poisson bracket of a quantity with the Hamiltonian describes the time evolution of that quantity as one moves along a curve in phase space. The Lie algebra structure of symmetries in mechanics is highlighted using this formulation. The classical propagator is derived using the Poisson bracket.

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50

Street, Brian. The Calder´on-Zygmund Theory II: Maximal Hypoellipticity. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.003.0002.

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This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted to this metric. The chapter has two major themes. The first is a more general reprise of the trichotomy described in Chapter 1 (Theorem 2.0.29). The second theme is a generalization of the fact that Euclidean singular integral operators are closely related to elliptic partial differential equations. The chapter also introduces a quantitative version of the classical Frobenius theorem from differential geometry. This “quantitative Frobenius theorem” can be thought of as yielding “scaling maps” which are well adapted to the Carnot–Carathéodory geometry, and is of central use throughout the rest of the monograph.

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