948 pages
Trim Size 6 1/2 X 9 7/16 in
Copyright 2011
Expected Release Date: Jun 2011 Hardcover, Reference
A title in the Handbook of the Philosophy of Science Series, Volume 10
Key Features
-Comprehensive coverage of all main theories in the philosophy of Complex Systems
-Clearly written expositions of fundamental ideas and concepts
-Definitive discussions by leading researchers in the field
-Summaries of leading-edge research in related fields are also included
The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on.
Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years.
675 pages
Copyright 2011
Hardcover, Reference
Expected Release Date: Jun 2011
Chapter 1. Introduction and Preliminaries
Chapter 2. The Zeta and Related Functions
Chapter 3. Series Involving Zeta Functions
Chapter 4. Evaluations and Series Representations
Chapter 5. Determinants of the Laplacians
Chapter 6. q-Extensions of some special functions and polynomials
Chapter 7. Miscellaneous Results
Bibliography
Author Information
By H. M. Srivastava, University of Victoria, Victoria, British Columbia, Canada and Jubesang Choi, Dongguk University, Gyeongju, Republic of Korea
CBMS-NSF Regional Conference Series in Applied Mathmatics
Paperback
ISBN: 9780898719390
150 pages
Dimensions: 247 x 174 mm
* Provides a presentation of the latest results on the existence and uniqueness of transmission eigenvalues for Maxwell's equations
* Gives a full discussion of uniqueness theorems in inverse electromagnetic scattering theory
* This is the only book that gives a complete description of the linear sampling method for electromagnetic waves
Preface
1. Inverse scattering in two dimensions
2. Maxwell's equations
3. The inverse problem for obstacles
4. The inverse scattering problem for anisotropic media
5. The inverse scattering problem for thin objects
6. The inverse scattering problem for buried objects
Bibliography
Index.
Series: London Mathematical Society Student Texts (No. 78)
ISBN: 9781107096387 Hardback
ISBN: 9781107422193 Paperback
70 exercises
Dimensions: 228 x 152 mm
available from May 2011
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah*Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background * including multilinear algebra, quadratic spaces and finite-dimensional real algebras * easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.
* Suitable for working mathematicians and physicists who work with Clifford algebras and their applications
* Chapters are self-contained to suit readers of various levels from undergraduate to professional
* Includes suggestions for further study
Introduction
Part I. The Algebraic Environment: 1. Groups and vector spaces
2. Algebras, representations and modules
3. Multilinear algebra
Part II. Quadratic Forms and Clifford Algebras: 4. Quadratic forms
5. Clifford algebras
6. Classifying Clifford algebras
7. Representing Clifford algebras
8. Spin
Part III. Some Applications: 9. Some applications to physics
10. Clifford analyticity
11. Representations of Spind and SO(d)
12. Some suggestions for further reading
Bibliography
Glossary
Index.
Paperback
ISBN: 9780521176835
73 b/w illus.
Dimensions: 228 x 152 mm
available from April 2011
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert*Zernike theorem, Babinet's principle and dipole arrays.
* A guide to a basic mathematical tool, emphasizing the practical applications of Fourier theory
* Now includes convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert*Zernike theorem, Babinet's principle and dipole arrays
* Demonstrates the technique through applications in optics, spectroscopy, electronics and telecommunications
1. Physics and Fourier transforms
2. Useful properties and theorems
3. Applications 1: Fraunhofer diffraction
4. Applications 2: signal analysis and communication theory
5. Applications 3: spectroscopy and spectral line shapes
6. Two-dimensional Fourier transforms
7. Multi-dimensional Fourier transforms
8. The formal complex Fourier transform
9. Discrete and digital Fourier transforms
10. Appendix
11. Bibliography
12. Index.