ISBN: 978-1-84265-459-0
Publication Year: September 2008
Pages: 266
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 630
This book presents in an elegant way, the essentials of two and three-dimensions of analytical geometry with plenty of examples to illustrate the basic ideas and to bequeath to the students the numerous techniques of problem-solving. The exercises provide ample problems to supplement steady progress and to broaden the intuition of generalization. The overall approach systematic, rigorous and least dependent on Euclidean propositions.
Metric Properties in Plane / Straight Lines in Plane / Circles in Plane / Conics in Plane / Metric Classification of Conics / Polar Coordinate System / Analytical Geometry (3D) / Plane / Straight Line / Locus, Surfaces and Curves / Answers to Exercises / Bibliography / Index.
Series: Frontiers in Applied Mathematics (No. 35)
Paperback (ISBN-13: 9780898716566)
Discontinous Galerkin (DG) methods for solving partial differential equations,
developed in the late 1990s, have become popular among computational scientists.
Covering both theory and computation, this book focuses on three primal
DG methods - the symmetric interior penalty Galerkin, incomplete interior
penalty Galerkin, and nonsymmetric interior penalty Galerkin - which are
variations of interior penalty methods. The author provides the basic tools
for analysis and discusses coding issues, including data structure, construction
of local matrices, and assembling of the global matrix. Computational examples
and applications to important engineering problems are also included. Part
I focuses on the application of DG methods to second order elliptic problems
in one dimension and in higher dimensions. Part II presents the time-dependent
parabolic problems - with and without convection. Part III contains applications
of DG methods to solid mechanics (linear elasticity), fluid dynamics (Stokes
and Navier*Stokes), and porous media *ow (two-phase and miscible displacement).
* Presents both theory and implementation, with detailed proofs and MATLABR codes provided in the appendices * Intended for numerical analysts, computational and applied mathematicians, and engineers. Also appropriate for a graduate or senior undergraduate course * Includes important applications for engineers from a variety of fields
List of figures; List of tables; List of algorithms; Preface; Part I. Elliptic Problems: 1. One-dimensional problem; 2. Higher dimensional problem; Part II. Parabolic Problems: 3. Purely parabolic problems; 4. Parabolic problems with convection; Part III. Applications: 5. Linear elasticity; 6. Stokes flow; 7. Navier-Stokes flow; 8. Flow in porous media; Appendix A. Quadrature rules; Appendix B. DG codes; Appendix C. An approximation result; Bibliography; Index.
Series: Cambridge Texts in Applied Mathematics (No. 44)
Paperback (ISBN-13: 9780521734905)
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
* No other book covers this range of subjects. * A valuable introductory text for mathematicians, scientists, engineers and computer scientists, featuring copious illustrations and structured exercises * The author’s clear and lively style make this rigorous text an enjoyable read
Preface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary differential equations: 1. Euler’s method and beyond; 2. Multistep methods; 3. Runge*Kutta methods; 4. Stiff equations; 5. Geometric numerical integration; 6. Error control; 7. Nonlinear algebraic systems; Part II. The Poisson equation: 8. Finite difference schemes; 9. The finite element method; 10. Spectral methods; 11. Gaussian elimination for sparse linear equations; 12. Classical iterative methods for sparse linear equations; 13. Multigrid techniques; 14. Conjugate gradients; 15. Fast Poisson solvers; Part III. Partial differential equations of evolution: 16. The diffusion equation; 17. Hyperbolic equations; Appendix. Bluffer’s guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index.
March 2008, 460 pp., hardcover
ISBN: 978-1-58603-782-6
Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and human. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of foundations of mathematics.
He is best known of the Kleene-Mostowski and Davis-Mostowski hierarchies of properties of integers reflecting the complexity of their definitions, and of the very elegant concept of a generalized quantifier which inspired and keeps stimulating a stream of deep work on fundamental issues of logics, deduction and reasoning both in mathematics and in computer science, and also of the contributions and excellent lectures on undecidability, unprovability, consistency and independence of various statements in set theory and arithmetic following Godel, Tarski and Cohen. The overall content of the volume is designed to cover the current main streams in the field.
For many years after WWII, especially in the late sixties, till his untimely death in 1975, Warsaw - where he led the centre of foundational studies - was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.
This volume is a collection of fifteen comprehensive research and expository articles, a complete bibliography of Andrzej Mostowski’s writings, three biographical and historical articles, and eleven short personal reminiscences, contributed by prominent researchers, all aimed at illuminating Andrzej Mostowski's ideas and personality.
Anyone wanting to see the roots of current applications of logic, be it in mathematics, computer science or philosophy, will find in this collection of articles plenty of helpful, stimulating and inspiring material both in science and about the social environment in which science is made.
Volume 16 NATO Science for Peace and Security Series: Information and Communication Security
June 2008, 356 pp., hardcover
ISBN: 978-1-58603-855-7
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields.
The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.