Bøger i Applied Mathematical Sciences serien

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds.

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes the fundamental ideas of the past two decades of research, carefully balancing theory and application.

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces.

This book introduces the area of inverse problems. It examines basic notions and difficulties encountered with ill-posed problems and presents two special nonlinear inverse problems in detail: the inverse spectral problem and the inverse scattering problem.

This treatment of pull-back attractors for non-autonomous Dynamical systems emphasizes the infinite-dimensional variety but also analyzes those that are finite. As a graduate primer, it covers everything from basic definitions to cutting-edge results.

This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their application for a number of nontrivial physical problems.

This mathematically rigorous survey of the special theory of relativity also details the physical significance of that mathematics. In addition to kinematics, particle dynamics and electromagnetic fields it treats subjects usually bypassed at elementary level.

This is an accessible text on the advanced symmetry methods for differential equations. Topics covered include conservation laws, Lie-Backlund symmetries, contact transformations, nonlocal symmetries, nonlocal mappings and non-classical method.

This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries.

At least when O is not too large, the fluid flow is nearly laminar and 2 the method of Couette is valuable because the torque is then proportional to 110 , where II is the kinematic viscosity of the fluid.

Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis models, and illustrates several new results in this field.

This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions.

Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics.

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions.

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a revision of the first edition of the averaging book. Updated chapters represent new insights in averaging and offer an effective entrance into this topic.

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

In the past several decades many significant results in averaging for systems of ODE's have been obtained.

This book is based on the author's experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines.

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD).

A complete resource on theory and computation, this book will be of interest to a range of practitioners, from mathematicians interested in prolate spheroidal wave functions as an analytical tool to electrical engineers designing filters and antennas.

Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.

This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds.

This book offers a detailed, rigorous, and self-contained presentation of the theory of hyperbolic conservation laws from the basic theory to the forefront of research. It contains details and information about numerical approximation for the Cauchy problem.

This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981).

Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry.

This book examines the main theorems in bifurcation theory. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces and shows how to apply the theory.

The revised edition of this systematic investigation of convection in systems comprised of liquid layers with deformatable interfaces offers new material on flows in ultra thin films. The text also reflects progress into dynamics of complex fluids.

This text gives a common treatment to three areas of application of global analysis to mathematical physics: the geometry of manifolds applied to classical mechanics; stochastic differential geometry used in quantum and statistical mechanics; and infinites-dimensional differential geometry.