Ralph Baierlein

Newton to Einstein:
The Trail of Light An Excursion to the Wave-Particle Duality & the Special Theory of Relativity

Description
This undergraduate text takes the reader along the trail of light from Newton’s particles to Einstein’s relativity. Like the best detective stories, it presents clues and encourages the reader to draw conclusions before the answers are revealed. The first seven chapters describe how light behaves, develop Newton’s particle theory, introduce waves and an electromagnetic wave theory of light, discover the photon, and culminate in the wave-particle duality. The book then goes on to develop the special theory of relativity, showing how time dilation and length contraction are consequences of the two simple principles on which the theory is founded. An extensive chapter derives the equation E = mc2 clearly from first principles and then explores its consequences and the misconceptions surrounding it. That most famous of issues arising from special relativity - the aging of the twins - is treated simply but compellingly.

Chapter Contents
Preface; 1. How light behaves; 2. Newton's particle theory; 3. A wave theory of light; 4. Interference; 5. Electromagnetic waves; 6. The photon; 7. The wave?particle duality; 8. Does the speed of light depend on the motion of the source of light?; 9. The principles of the Special Theory of Relativity; 10. Time dilation and length contraction; 11. E=mc2; 12. The twins; 13. The Lorentz transformations; 14. Space and time; Glossary; Appendices; Index.

ISBN: 0-521-42323-6
Binding: Paperback
Pages: 345
Published: 16 August 2001

J. F. James

A Student's Guide to Fourier Transforms
With Applications in Physics and Engineering (2nd edition)

Description
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular 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-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.

Chapter Contents
1. Physics and Fourier transforms; 2. Useful properties and theorems; 3. Applications I: Fraunhofer diffraction; 4. Applications II: communication theory; 5. Applications III: spectroscopy; 6. Two-dimensional transforms; 7. Multi-dimensional transforms; 8. The formal complex Fourier transform; 9. Discrete and digital Fourier transforms; Appendix: mathematical proofs.

ISBN: 0-521-80826-X
Binding: Hardback
ISBN: 0-521-00428-4
Binding: Paperback
Pages: 150
available from April 2002

Arkady Pikovsky, Michael Rosenblum, Jurgen Kurths

Synchronization
A Universal Concept in Nonlinear Science

Cambridge Nonlinear Science Series series

Description
Synchronization phenomena are abundant in science, nature, engineering and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is also outlined. The second half of the book presents the main effects of synchronization in a rigorous and systematic manner, describing both classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering, and natural sciences.

Chapter Contents
1. Introduction; Part I. Synchronization Without Formulae: 2. Basic notions: self-sustained oscillator and its phase; 3. Synchronization of a periodic oscillator by external force; 4. Synchronization of two and many oscillators; 5. Synchronization of chaotic systems; 6. Detecting synchronization in experiments; Part II. Phase Locking and Frequency Entrainment: 7. Synchronization of periodic oscillators by periodic external action; 8. Mutual synchronization of two interacting periodic oscillators; 9. Effect of noise on phase locking; 10. Phase synchronization of chaotic systems; 11. Synchronization in oscillatory media; 12. Populations of globally coupled oscillators; Part III. Synchronization of Chaotic Systems: 13. Complete synchronization I: basic concepts; 14. Complete synchronization II: generalizations and complex systems; 15. Synchronization of complex dynamics by external forces; Appendix 1. Discovery of synchronization by Christiaan Huygens; Appendix 2. Instantaneous phase and frequency of a signal; Index.

ISBN: 0-521-59285-2
Binding: Hardback
Pages: 432
available from October 2001

Robert B. Griffiths

Consistent Quantum Theory

Description

Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born’s probabilistic interpretation with Schrodinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrodinger’s cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnes. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

Chapter Contents

1. Introduction; 2. Wave functions; 3. Linear algebra in Dirac notation; 4. Physical properties; 5. Probabilities and physical variables; 6. Composite systems and tensor products; 7. Unitary dynamics; 8. Stochastic histories; 9. The Born rule; 10. Consistent histories; 11. Checking consistency; 12. Examples of consistent families; 13. Quantum interference; 14. Dependent (contextual) events; 15. Density matrices; 16. Quantum reasoning; 17. Measurements I; 18. Measurements II; 19. Coins and counterfactuals; 20. Delayed choice paradox; 21. Indirect measurement paradox; 22. Incompatibility paradoxes; 23. Singlet state correlations; 24. EPR paradox and Bell inequalities; 25. Hardy’s paradox; 26. Decoherence and the classical limit; 27. Quantum theory and reality; Bibliography.

ISBN: 0-521-80349-7
Binding: Hardback
Pages: 416
available from December 2001

William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery

Numerical Recipes in C++
The Art of Scientific Computing
(2nd edition)

Description
Now the acclaimed Second Edition of Numerical Recipes is available in the C++ object-oriented programming language. Including and updating the full mathematical and explanatory contents of Numerical Recipes in C, this new version incorporates completely new C++ versions of the more than 300 Numerical Recipes routines that are widely recognized as the most accessible and practical basis for scientific computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. Highlights include linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations and inverse theory. The authors’ approach to C++ preserves the efficient execution that C users expect, while simultaneously employing a clear, object-oriented interface to the routines. Tricks and tips for scientific computing in C++ are liberally included. The routines, in ANSI/ISO C++ source code, can thus be used with almost any existing C++ vector/matrix class library, according to user preference. A simple class library for stand-alone use is also included in the book. Both scientific programmers new to C++, and experienced C++ programmers who need access to the Numerical Recipes routines, can benefit from this important new version of an invaluable, classic text.

Chapter Contents
1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Integration of ordinary differential equations; 17. Two point boundary value problems; 18. Integral equations and inverse theory; 19. Partial differential equations; 20. Less-numerical algorithms; References.

ISBN: 0-521-75033-4
Binding: Hardback
Pages: 1064
available from March 2002