Integral equations in the classical theory of fluids
Author: Michael Wertheim
Publisher:
Published: 1972
Total Pages: 150
ISBN-13:
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The Classical Theory of Integral Equations
Author: Stephen M. Zemyan
Publisher: Springer Science & Business Media
Published: 2012-07-10
Total Pages: 350
ISBN-13: 0817683496
DOWNLOAD EBOOKThe Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.
Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
Author: J. R. Solana
Publisher: CRC Press
Published: 2013-03-22
Total Pages: 400
ISBN-13: 1439807760
DOWNLOAD EBOOKPerturbation theory forms an important basis for predicting the thermodynamic characteristics of real fluids and solids. This book provides a comprehensive review of current perturbation theories-as well as integral equation theories and density functional theories-for the equilibrium thermodynamic and structural properties of classical systems. Emphasizing practical applications, the book avoids complex theoretical derivations as much as possible. Appropriate for experienced researchers as well as postgraduate students, the text presents a wide-ranging yet detailed view and provides a useful guide to the application of the theories described.
Integral Equation Theory Description of Phase Equilibria in Classical Fluids
Author: C. Caccamo
Publisher:
Published: 1996
Total Pages: 106
ISBN-13:
DOWNLOAD EBOOKIntegral Equations
Author: Harry Hochstadt
Publisher: John Wiley & Sons
Published: 2011-09-09
Total Pages: 282
ISBN-13: 1118165934
DOWNLOAD EBOOKThis classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.
Singular Integral Equations
Author: E.G. Ladopoulos
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 569
ISBN-13: 3662042916
DOWNLOAD EBOOKThe present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.
Classical Liquids
Author: Riccardo Fantoni (t.d.-)
Publisher:
Published: 2003
Total Pages:
ISBN-13:
DOWNLOAD EBOOKLinear Integral Equations
Author: Ram P. Kanwal
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 311
ISBN-13: 1483262502
DOWNLOAD EBOOKLinear Integral Equations: Theory and Technique is an 11-chapter text that covers the theoretical and methodological aspects of linear integral equations. After a brief overview of the fundamentals of the equations, this book goes on dealing with specific integral equations with separable kernels and a method of successive approximations. The next chapters explore the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. These topics are followed by discussions of the symmetric kernels, singular integral equations, and the integral transform methods. The final chapters consider the applications of linear integral equations to mixed boundary value problems. These chapters also look into the integral equation perturbation methods. This book will be of value to undergraduate and graduate students in applied mathematics, theoretical mechanics, and mathematical physics.
Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems
Author: D. B. Ingham
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 165
ISBN-13: 3642823300
DOWNLOAD EBOOKHarmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.
Partial Differential Equations in Fluid Mechanics
Author: Charles L. Fefferman
Publisher: Cambridge University Press
Published: 2018-09-27
Total Pages: 339
ISBN-13: 1108573592
DOWNLOAD EBOOKThe Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
