الصفحة 10
الصفحة 10
Geometric numerical integration : Structure-preserving algorithms for ordinary differential equations
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
Geometric Modeling and Algebraic Geometry
The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side.
Geometric mechanics on riemannian manifolds : Applications to partial differential equations
This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. It includes : Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves.
Geometric Integration Theory
This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics
Geometric Group Theory ; Geneva and Barcelona Conferences
This volume assembles research papers in geometric and combinatorial group theory. This wide area may be defined as the study of those groups that are defined by their action on a combinatorial or geometric object, in the spirit of Klein’s programme.The contributions range over a wide spectrum: limit groups, groups associated with equations, with cellular automata, their structure as metric objects, their decomposition, etc. Their common denominator is the language of group theory, used to express and solve problems ranging from geometry to logic.
Geometric Function Theory : Explorations in Complex Analysis
Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.
Generalized collocations methods : Solutions to nonlinear problems
This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution. Based on a unified approach combining modeling, mathematical methods, and scientific computation, each chapter begins with several examples and problems solved by computational methods; full details of the solution techniques used are given. The last section of each chapter provides problems and exercises giving readers the opportunity to practice using the mathematical tools already presented.
General Relativity
this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle.
Galerkin Finite Element Methods for Parabolic Problems
This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution.
Fuzzy Implications
Fuzzy Implications (FIs) generalize the classical implication and play a similar important role in Fuzzy Logic (FL), both in FL_n and FL_w in the sense of Zadeh. Their importance in applications of FL, viz., Approximate Reasoning (AR), Decision Support Systems, Fuzzy Control (FC), etc., is hard to exaggerate. This treatise is perhaps the first attempt at dealing exclusively with this class of operations.
Fuzzy Equational Logic
The book deals with similarity relations defined on a set with functions. The functions are required to map similar elements to similar ones. The book presents basic mathematical properties of structures consisting of similarity-preserving functions and logics for reasoning about similarities. The presented text is self-contained. The notions and results are demonstrated through examples which are graphically illustrated. The book is useful for researchers, but it can also be used as a graduate text.
Fundamentals of Structural Dynamics
Explains foundational concepts and principles surrounding the theory of vibrations and gives equations of motion for complex systems. The book presents classical vibration theory in a clear and systematic way, detailing original work on vehicle-bridge interactions and wind effects on bridges. Chapters give an overview of structural vibrations, including how to formulate equations of motion, vibration analysis of a single-degree-of-freedom system, a multi-degree-of-freedom system, and a continuous system, the approximate calculation of natural frequencies and modal shapes, and step-by-step integration methods. Each chapter includes extensive practical examples and problems.
Fundamentals of Cavitation
Treats cavitation, which is a unique phenomenon in the field of hyd- dynamics, although it can occur in any hydraulic machinery such as pumps, propellers, artificial hearts, and so forth. Cavitation is generated not only in water, but also in any kind of fluid, such as liquid hydrogen. The generation of cavitation can cause severe damage in hydraulic machinery. Therefore, the prevention of cavitation is an important concern for designers of hydraulic machinery. On the contrary, there is great potential to utilize cavitation in various important applications, such as environmental protection. There have been several books published on cavitation, including one by the same authors. This book differs from those previous ones, in that it is both more physical and more theoretical. Any theoretical explanation of the cavitation phenomenon is rather difficult, but the authors have succeeded in explaining it very well, and a reader can follow the equations easily. It is an advantage in reading this book to have some understanding of the physics of cavitation. Therefore, this book is not an introductory text, but a book for more advanced study. However, this does not mean that this book is too difficult for a beginner, because it explains the cavitation phenomenon using many figures. Therefore, even a beginner on cavitation can read and can understand what cavitation is.
Fundamental Numerical Methods for Electrical Engineering
The book presents fundamental numerical methods which are most frequently applied in the electrical (electronic) engineering. All methods discussed are illustrated with real-world examples of applications. It is shown how real engineering questions can be transformed into the corresponding mathematical problems and next effectively solved by using appropriate numerical methods.
Functions de variable réelle : Théorie élémentaire = Real variable functions : Elementary theory
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This Book is the fourth of the treaty; it is devoted to the basics of real analysis. It includes the chapters: Derivatives; Primitive and integral; Elementary functions; Differential equations ; Local study of functions; Generalized Taylorian developments. Euler-Maclaurin summation formula; The gamma function. It also contains historical notes.
Functional Equations and How to Solve Them
This book covers topics in the theory and practice of functional equations. Special emphasis is given to methods for solving functional equations that appear in mathematics contests, such as the Putnam competition and the International Mathematical Olympiad. This book will be of particular interest to university students studying for the Putnam competition, and to high school students working to improve their skills on mathematics competitions at the national and international level. Mathematics educators who train students for these competitions will find a wealth of material for training on functional equations problems.
Functional Analysis and Evolution Equations : The Günter Lumer Volume
Günter Lumer was an outstanding mathematician whose work has great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips of 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Günter Lumer.
Fuchsian Reduction : Applications to Geometry, Cosmology, and Mathematical Physics
Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail.
Frontiers of Numerical Analysis : Durham 2004
Contains lecture notes on four topics at the forefront of research in computational mathematics. This book presents a self-contained guide to a research area, an extensive bibliography, and proofs of the key results. It is suitable for professional mathematicians who require an accurate account of research in areas parallel to their own.
From Stochastic Calculus to Mathematical Finance : The Shiryaev Festschrift
The Festschrift is a collection of papers, including several surveys, written by his former students, co-authors and colleagues. These reflect the wide range of scientific interests of the teacher and his Moscow school. The topics range from the disorder problems to stochastic calculus and their applications to mathematical economics and finance. A full biobibliography of Shiryaev's works is included. The book represents the modern state of art of many aspects of a quickly maturing theory and will be an essential source and reading for researchers in this area.
