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This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics.This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of stronglystable systems.With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.

The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions.

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 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 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.

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 work aims to introduce students to active areas of research in mathematical physics in a rather direct way, thus minimizing the use of abstract mathematics. The book's main features are geometric methods in spectral analysis, semi-classical analysis of resonance and other topics.

By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course.

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems.

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 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.

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.

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.

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.

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 text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm.

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).

On the other hand, satellite observations of our own planet on a daily and hourly basis have turned it into a unique laboratory for the study of fluid motions on a scale never dreamt of before: the motion of cyclones can be observed via satellite just as wing tip vortices are studied in a wind tunnel.

Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

This book is a very well-accepted introduction to the subject. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy's example of a linear equation without solutions.

This book presents core material in nonlinear analysis, offering working knowledge of manifolds, dynamical systems, tensors and differential forms. Coverage includes Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory.

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations.

This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results.

The 2nd edition presents image analysis applications, outlines their precise mathematics and shows how to discretize them. It reviews progress in image processing applications covered by the PDE framework, and updates the existing material. Also provides programming tools for creating simulations.

This book is developed for the study of vectorial problems in the calculus of variations. It is a new edition of the earlier book published in 1989. Almost half of the book consists of new material and there are added examples.

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns.

With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.

The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations.

This book examines the basic mathematical properties of solutions to boundary integral equations and details the variational methods for the boundary integral equations arising in elasticity, fluid mechanics and acoustic scattering theory.

I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space.