Although the application of differential equations to
economics is a vast and vibrant area, the subject has not been
systematically studied; it is often treated as a subsidiary part
of mathematical economics textbooks. This book aims to fill that
void by providing a unique blend of the theory of differential
equations and their exciting applications to dynamic economics.
Containing not just a comprehensive introduction to the
applications of the theory of linear (and linearized)
differential equations to economic analysis, the book also
studies nonlinear dynamical systems, which have only been widely
applied to economic analysis in recent years. It provides
comprehensive coverage of the most important concepts and
theorems in the theory of differential equations in a way that
can be understood by any reader who has a basic knowledge of
calculus and linear algebra. In addition to traditional
applications of the theory to economic dynamics, the book
includes many recent developments in different fields of
economics.
Contents:
Dimension One:
Scalar Linear Differential Equations
Scalar Nonlinear Differential Equations
Economic Evolution with Scalar Differential Equations
Dimension Two:
Planar Linear Differential Equations
Planar Nonlinear Differential Equations
Planar Dynamical Economical Systems
Higher Dimensions:
Higher-Dimensional Differential Equations
Higher-Dimensional Nonlinear Differential Equations
Higher-Dimensional Economic Evolution
Epilogue: Economic Evolution with Changeable Speeds and
Structures
Readership: Economists and scientists of other disciplines who
are concerned with modeling and understanding the time evolution
of nonlinear dynamic economic systems.
500pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-333-4
This book covers comprehensive bifurcation theory and its
applications to dynamical systems and partial differential
equations (PDEs) from science and engineering, including in
particular PDEs from physics, chemistry, biology, and
hydrodynamics.
The book first introduces bifurcation theories recently developed
by the authors, on steady state bifurcation for a class of
nonlinear problems with even order nondegenerate nonlinearities,
regardless of the multiplicity of the eigenvalues, and on
attractor bifurcations for nonlinear evolution equations, a new
notion of bifurcation.
With this new notion of bifurcation, many longstanding
bifurcation problems in science and engineering are becoming
accessible, and are treated in the second part of the book. In
particular, applications are covered for a variety of PDEs from
science and engineering, including the Kuramoto?Sivashinsky
equation, the Cahn?Hillard equation, the Ginzburg?Landau
equation, reaction-diffusion equations in biology and chemistry,
the Benard convection problem, and the Taylor problem. The
applications provide, on the one hand, general recipes for other
applications of the theory addressed in this book, and on the
other, full classifications of the bifurcated attractor and the
global attractor as the control parameters cross certain critical
values, dictated usually by the eigenvalues of the linearized
problems. It is expected that the book will greatly advance the
study of nonlinear dynamics for many problems in science and
engineering.
Contents:
Introduction to Steady State Bifurcation
Introduction to Dynamic Bifurcation
Reduction Procedures and Stability
Steady State Bifurcation
Dynamic Bifurcation Theory: Finite Dimensional Case
Dynamic Bifurcation Theory: Infinite Dimensional Case
Bifurcation of Nonlinear Elliptic Equations
Reaction-Diffusion Equations
Pattern Formation and Wave Equations
Fluid Dynamics
Readership: Graduate students and researchers in mathematics,
physics, chemistry, biology and engineering.
350pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-287-7
ISBN 981-256-352-0(pbk)
Standard textbooks on the many-body problem do not include a
wealth of valuable experimental data, in particular recent
results from direct knockout reactions, which are directly
related to the single-particle propagator in many-body theory. In
this indispensable book, the comparison with experimental data is
incorporated from the start, making the abstract concept of
propagators vivid and comprehensible. The discussion of numerical
calculations using propagators or Green's functions, also absent
from current textbooks, is presented in this book. Much of the
material has been tested in the classroom and the introductory
chapters allow a seamless connection with a one-year graduate
course in quantum mechanics. While the majority of books on many-body
theory deal with the subject from the viewpoint of condensed
matter physics, this book also emphasizes finite systems and
should be of considerable interest to researchers in nuclear,
atomic, and molecular physics. A unified treatment of many
different many-body systems is presented using the approach of
self-consistent Green's functions. Several topics, not available
in other books, in particular the description of atomic
Bose?Einstein condensates, have been included.
The coverage proceeds in a systematic way from elementary
concepts, such as second quantization and mean-field properties,
to a more advanced but self-contained presentation of the physics
of atoms, molecules, nuclei, nuclear and neutron matter, electron
gas, quantum liquids, atomic Bose?Einstein and fermion
condensates, and pairing correlations in finite and infinite
systems.
Contents:
Identical Particles
Second Quantization
Independent-Particle Model for Fermions in Finite Systems
Two-Particle States and Interactions
Noninteracting Bosons and Fermions
Propagators in One-Particle Quantum Mechanics
Single-Particle Propagator in the Many-Body System
Perturbation Expansion of the Single-Particle Propagator
Dyson Equation and Self-Consistent Green's Functions
Mean-Field or Hartree?Fock Approximation
Beyond the Mean-Field Approximation
Interacting Boson Systems
Excited States in Finite Systems
Excited States in Infinite Systems
Excited States in N ? 2 Systems and In-Medium Scattering
Dynamical Treatment of the Self-Energy in Infinite Systems
Dynamical Treatment of the Self-Energy in Finite Systems
Bogoliubov Perturbation Expansion for the Bose Gas
Boson Perturbation Theory Applied to Physical Systems
In-Medium Interaction and Scattering of Dressed Particles
Conserving Approximations and Excited States
Pairing Phenomena
Readership: Advanced graduate students in quantum mechanics of
many-body systems, researchers working on finite and infinite
quantum many-body systems like atoms, molecules, Bose?Einstein
condensates, nuclei, nuclear matter, neutron matter, electron gas
and quantum liquids.
752pp Pub. date: Apr 2005
ISBN 981-256-294-X
ISBN 981-256-350-4(pbk)
Chaos, Fractals, Cellular Automata, Neural Networks, Genetic
Algorithms, Gene Expression Programming, Support Vector Machine,
Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and
SymbolicC++ Programs
(3rd Edition)
The study of nonlinear dynamical systems has advanced
tremendously in the last 20 years, making a big impact on science
and technology. This book provides all the techniques and methods
used in nonlinear dynamics. The concepts and underlying
mathematics are discussed in detail.
The numerical and symbolic methods are implemented in C++,
SymbolicC++ and Java. Object-oriented techniques are also applied.
The book contains more than 150 ready-to-run programs.
The text has also been designed for a one-year course at both the
junior and senior levels in nonlinear dynamics. The topics
discussed in the book are part of e-learning and distance
learning courses conducted by the International School for
Scientific Computing.
Contents:
Nonlinear and Chaotic Maps
Time Series Analysis
Autonomous Systems in the Plane
Nonlinear Hamilton Systems
Nonlinear Dissipative Systems
Nonlinear Driven Systems
Controlling and Synchronization of Chaos
Fractals
Cellular Automata
Solving Differential Equations
Neural Networks
Genetic Algorithms
Gene Expression Programming
Optimization
Discrete Wavelets
Discrete Hidden Markov Models
Fuzzy Sets and Fuzzy Logic
Readership: Undergraduates, graduate students and researchers in
computer science, engineering, mathematics, theoretical and
computational physics.
608pp Pub. date: Mar 2005
ISBN 981-256-278-8
ISBN 981-256-291-5(pbk)
Traditionally, non-quantum physics has been concerned with
deterministic equations where the dynamics of the system are
completely determined by initial conditions. A century ago the
discovery of Brownian motion showed that nature need not be
deterministic. However, it is only recently that there has been
broad interest in nondeterministic and even chaotic systems, not
only in physics but in ecology and economics. On a short term
basis, the stock market is nondeterministic and often chaotic.
Despite its significance, there are few books available that
introduce the reader to modern ideas in stochastic systems. This
book provides an introduction to this increasingly important
field and includes a number of interesting applications.
Contents:
Stochastic Variables and Stochastic Processes
Stochastic Differential Equations
The Fokker?Planck Equation
Advanced Topics
Numerical Solutions for Ordinary Stochastic Differential
Equations
Readership: Researchers and graduate students in physics,
chemistry, and engineering.
200pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-296-6