Symmetry Problems. the Navier-Stokes Problem. (Synthesis Lectures on Mathematics and Statistics)
by Alexander G. Ramm
This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equatio...
The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem.
A Treatise on the Calculus of Finite Differences (Classic Reprint)
by George Boole
200 Worksheets - Word Names for 10 Digit Numbers (200 Days Math Number Name, #9)
by Kapoo Stem
Hilbert Space Methods in Science and Engineering,
This volume aims to present Hilbert space theory as an accessible language for applied mathematicians, engineers and scientists. A knowledge of linear algebra and analysis is assumed. The construction of mathematical models using Hilbert space theory is illustrated with problems and results are evaluated. For the first time, mathematical models based on reproducing kernel Hilbert spaces and causal operators are explained at an introductory level.
Fluid-Structure Interaction (Radon Series on Computational and Applied Mathematics)
This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreo...
This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The first volume mainly presents basic concepts and the theoretical background. Differential (ordinary and partial) equations and relevant topics are discussed in detail.
Graph Paper Notebook 1 inch Squares (Graph Book for Math, #1)
by Roger Wells
'This booklet provides a very lucid and versatile introduction to the methods of linear partial differential equations. It covers a wealth of very important material in a concise, nevertheless very instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this area of both classical and contemporary mathematics.'zbMATHPartial differential equations arise in many branches of science and they vary in many ways. No one method can be used to...
Hyperfunctions and Pseudo-Differential Equations
by Hikosaburo Komatsu
First Course In Partial Differential Equations, A
by J Robert Buchanan and Zhoude Shao
This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear PDEs, the heat equation, wave equation, and Laplace's equation. First-order and some common nonlinear PDEs arising in the physical and li...
Infinite-dimensional Dynamical Systems In Atmospheric And Oceanic Science
by Boling Guo and Daiwen Huang
The book provides some recent works in the study of some infinite-dimensional dynamical systems in atmospheric and oceanic science. It devotes itself to considering some infinite-dimensional dynamical systems in atmospheric and oceanic science, especially in geophysical fluid dynamics. The subject on geophysical fluid dynamics mainly tends to focus on the dynamics of large-scale phenomena in the atmosphere and the oceans. One of the important contents in the dynamics is to study the infinite-dim...
Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scatt...
Asymptotic Issues For Some Partial Differential Equations
by Michel Marie Chipot
Much progress has been made in recent years on the issue of asymptotic behavior of problems set in cylinders. This book goes one step further by presenting the latest accomplishments on asymptotic behavior in domains which become unbounded.It also investigates new issues which have emerged including existence and uniqueness of solution in unbounded domains, anisotropic singular perturbations, periodic behavior forced by periodic data. These new advances are treated with original techniques devel...
Matrix-Based Multigrid (Numerical Methods and Algorithms, #2)
by Yair Shapira
Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical...
This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.
Singular Elliptic Problems (Oxford Lecture Series in Mathematics and Its Applications)
by Marius Ghergu and Vicentiu RADULESCU
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relev...
In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivati...
Numerical Solution of Partial Differential Equations in Science and Engineering
by Leon Lapidus and George F. Pinder
From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject ...[It] is unique in that it covers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail ...Numerous practical examples and applications ar...
Time-Frequency Analysis of Operators (de Gruyter Studies in Mathematics, #75)
by Elena Cordero and Luigi Rodino
This authoritative text studies pseudo-differential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of Gabor representations for certain classes of dispersive equations. Moreover, modulation spaces are employed to study dispersive equations such as the Schroedinger, wave, and Klein-Gordon equations.
The Finite Difference Method in Partial Differential Equations
by A Richard Mitchell and D. F. Griffiths
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or precon...
Geometric Theory of Generalized Functions with Applications to General Relativity
This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: the first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singu...