2009, Approx. 230 p., Hardcover
ISBN: 978-3-642-00540-4
Due: May 2009
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics.
Jurgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Researchers, graduate and upper undergraduate students in geometry and in theoretical/mathematical physics
Table of contents
1.Geometry.- 1.1.Riemannian and Lorentzian manifolds.- 1.2.Bundles and connections.- 1.3.Tensors and spinors.- 1.4.Riemann surfaces and moduli spaces.- 1.5.Supermanifolds.- 2.Physics.- 2.1.Classical and quantum physics.- 2.2.Lagrangians.-2.3.Variational aspects.- 2.4.The sigma model.- 2.5.Functional integrals.- 2.6.Conformal field theory.- 2.7.String theory.- Bibliography.- Index.
2009, 160 p., Hardcover
ISBN: 978-3-642-00613-5
The method of wavelet transforms is one key tool in signal processing and control. Modern wavelet theory defines outlines for construction of wavelets and transformations using them. It gives rules that one has to obey to get a wavelet basis with desired properties, meaning that everyone can create a wavelet adequate for the given task. An oscillatory property and multiresolution nature of wavelets recommends them for use both in signal processing and in solving complex mathematical models of real world phenomena.
This book brings to engineers and other practitioners help in understanding how wavelets work in order to be able to create new or modify the existing wavelets according to their needs and tries to satisfy different user groups. It is self contained and no previous knowledge is assumed.
In seven chapters, the book gives a concise understanding of the theory of wavelets, explains how to compute them in practise and finally presents typical applications of wavelets and how they work. The book is written for graduate students and practising Engineers of electrical communications, signal processing and control.
Graduate students and practicing engineers of electrical communications, signal processing and control
Introduction.- Least-Squares Approximation.- Multiresolution.- Wavelets.- How to Compute.- Analogy with Filters.- Applications.
2009, Approx. 215 p. 96 illus. in color., Hardcover
ISBN: 978-1-84882-378-5
Due: July 2009
Uses 3D colour drawings and tabulations of algebraic expansions to reveal a new way of looking at the algebra
The true power of vectors has never been exploited, for over a century, mathematicians, engineers, scientists, and more recently programmers, have been using vectors to solve an extraordinary range of problems. However, today, we can discover the true potential of oriented, lines, planes and volumes in the form of geometric algebra. As such geometric elements are central to the world of computer games and computer animation, geometric algebra offers programmers new ways of solving old problems.
John Vince (best-selling author of a number of books including Geometry for Computer Graphics, Vector Analysis for Computer Graphics and Geometric Algebra for Computer Graphics) provides new insights into geometric algebra and its application to computer games and animation.
The first two chapters review the products for real, complex and quaternion structures, and any non-commutative qualities that they possess. Chapter three reviews the familiar scalar and vector products and introduces the idea of edyadicsf, which provide a useful mechanism for describing the features of geometric algebra. Chapter four introduces the geometric product and defines the inner and outer products, which are employed in the following chapter on geometric algebra. Chapters six and seven cover all the 2D and 3D products between scalars, vectors, bivectors and trivectors. Chapter eight shows how geometric algebra brings new insights into reflections and rotations, especially in 3D. Finally, chapter nine explores a wide range of 2D and 3D geometric problems followed by a concluding tenth chapter.
Filled with lots of clear examples, full-colour illustrations and tables, this compact book provides an excellent introduction to geometric algebra for practitioners in computer games and animation.
Introduction.- Products.- Vector Products.- The Geometric Product.- Geometric Algebra.- Products in 2D.- Products in 3D.- Reflections and Rotations.- Applied Geomteric Algebra.- Conclusion.- Appendices.
Series: Texts in Applied Mathematics , Vol. 39
2009, Approx. 600 p., Hardcover
ISBN: 978-1-4419-0457-7
Due: July 2009
Covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis
Exercises at the end of most sections are included (419)
Short discussion of the literature, including recommendations for additional reading is provided at the end of each chapter
This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, boundary integral equations for planar regions, and multivariable polynomial approximations. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. In this third edition, a new chapter, Multivariable Polynomial Approximations, is included, numerous changes are made throughout the entire text, and new exercises are added.
Linear Spaces.- Linear Operators on Normed Spaces.- Approximation Theory.- Fourier Analysis and Wavelets.- Nonlinear Equations and Their Solution by Iteration.- Finite Difference Method.- Sobolev Spaces.- Weak Formulations of Elliptic Boundary Value Problems.- The Galerkin Method and Its Variants.- Finite Element Analysis.- Elliptic Variational Inequalities and Their Numerical Approximations.- Numerical Solution of Fredholm Integral Equations of the Second Kind.- Boundary Integral Equations.- Multivariable Polynomial Approximations.- References.- Index.
Series: Applied and Numerical Harmonic Analysis
2009, Approx. 410 p. 14 illus., Hardcover
ISBN: 978-0-8176-4802-2
Due: September 2009
A wide variety of problems in engineering and applied science can be formulated as continuous-time stochastic processes, i.e., differential equations with noisy forcing. Noise also enters prominently in information theory, which is concerned with communication, statistical estimation, and the extraction of patterns in the presence of noise.
The topic of Lie groups also enters into engineering and the physical sciences in a variety of ways. For example, problems involving the motion of rigid bodies are naturally described using methods from differential geometry and the theory of Lie groups.
The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique textbook presents these topics in a unified setting, thereby building bridges between fields that are rarely studied by the same individuals.
Volume I establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, and the statistical branch of information theory. Volume 2 delves into deeper relationships between these topics, including stochastic geometry, geometrical aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups.
Preface.- Introduction.- Gaussian Distributions and the Heat Equation.- Probability and Information Theory.- Stochastic Differential Equations.- Geometry of Curves and Surfaces.- Differential Forms.- Polytopes and Manifolds.- Stochastic Processes on Manifolds.- Summary.- Appendix. Review of Linear Algebra, Vector Calculus, and Systems Theory.- Index.