This book is devoted to the numerical computation of linear and nonlinear differential equations, and their mathematical theory and applications. The contributed papers reflect the interest and high research level of the Chinese mathematicians working in these fields.

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.

This book covers a broad spectrum of the most important, basic numerical and analytical techniques used in physics -including ordinary and partial differential equations, linear algebra, Fourier transforms, integration and probability. Now language-independent. Features attractive new 3-D graphics. Offers new and significantly revised exercises. Replaces FORTRAN listings with C++, with updated versions of the FORTRAN programs now available on-line. Devotes a third of the book to partial differential equations-e.g., Maxwell's equations, the diffusion equation, the wave equation, etc. This numerical analysis book is designed for the programmer with a physics background. Previously published by Prentice Hall / Addison-Wesley

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.

This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.

Presents the proceedings of the recently held conference at the University of Plymouth. Papers describe recent work by leading researchers in twistor theory and cover a wide range of subjects, including conformal invariants, integral transforms, Einstein equations, anti-self-dual Riemannian 4-manifolds, deformation theory, 4-dimensional conformal structures, and more.;The book is intended for complex geometers and analysts, theoretical physicists, and graduate students in complex analysis, complex differential geometry, and mathematical physics.

Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.

Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets, disconnected numbers and quotient maps.;Explaining the definitions and techniques used in the two fields and providing results from both areas, this volume: examines prime end (accessible) rotation numbers for chaotic sets and Henon maps; discussed the connection between the rotation shadowing property and the structure of the rotation set for annulus homeomorphisms; offers a Nielson-type theorum concerning the minimum number of fixed points for an area preserving homeomorphism of the two disc; constructs a closed unit disc that admits many inequivalent homeomorphisms that are Denjoy on the boundary and distinct irrational rotations on the interior; gives a geometric description of a horseshoe-type mapping of a plane disc into itself whose attracting set is not chainable; and considers semigroups generated by maps topologically conjugate to contractions.;Written by experts who provide a cross-disciplinary perspective, this volume is intended for applied mathematicians, topologists, geomesters, physicists and graduate-level students in these disciplines.