(Hardback)
0-19-850688-0
Publication date: July 2003
294 pages, 15, 234mm x 156mm
Series: Oxford Statistical Science Series
Excellent balance of theory and applications
Extensively illustrated
Diverse applications are described
Description
This book provides a comprehensive study
of nonlinear estimating
equations and artificial likelihoods for
statistical inference.
It includes a variety of examples from practical
applications and
is ideal for research statisticians and advanced
graduate
students.
Readership:
Researchers and advanced students in statistics
and applied
sciences seeking a comprehensive study of
nonlinear estimating
equations and artificial likelihoods for
statistical inference.
Contents/contributors
Introduction
Estimating functions
Numerical algorithms
Working with roots
Methodologies for root selection
Artificial likelihoods and estimating functions
Root selection and dynamical systems
Bayesian estimating functions
Bibliography
Index
April 2003, ISBN 0-306-47748-3, Hardbound
This book is intended to serve as a text
for both beginning and
second courses in complex analysis of functions
of one complex
variable. The material that is appropriate
for more advanced
study is developed from elementary material.
The concepts are
illustrated with large numbers of examples,
many of which involve
problems students encounter in other courses.
For example,
students who have taken an introductory physics
course will have
encountered analysis of simple AC circuits.
This text revisits
such analysis using complex numbers. Cauchy's
residue theorem is
used to evaluate many types of definite integrals
that students
are introduced to in the beginning calculus
sequence. Methods of
conformal mapping are used to solve problems
in electrostatics.
The book contains material that is not considered
in other
popular complex analysis texts. For example,
one chapter is
devoted to an analysis of multivalued functions,
with
applications to the evaluation of certain
types of integrals.
Another chapter deals with the singularity
structure of functions
that are defined by integrals which cannot
be evaluated in terms
of elementary functions. A third chapter
develops dispersion
relations, which are mathematical tools for
determining a
complete function from a knowledge of just
the real part, or just
the imaginary part of the function.
Contents
1. Introduction. 2. Complex Numbers. 3. Complex
Variables. 4.
Series, Limits and Residues. 5. Evaluation
of Integrals. 6.
Multivalued Functions, Branch Points and
Cuts. 7. Singularities
of Functions Defined by Integrals. 8. Conformal
Mapping. 9.
Dispersion Relations. Appendix 1: Derivation
of Green's Theorem.
Appendix 2: Derivation of the Geometric Series.
Appendix 3:
Evaluation of an Integral. Appendix 4: Transformation
of
Laplace's Equation. Appendix 5: Transformation
of Boundary
Conditions. Index.
200 pages, 9x6 inches
April 2003 softcover
ISBN 1-58949-026-6
Contents:
1. Relativity and Quantization
2. Charged Particle in Electromagnetic Field
3. Dirac Hydrogen Atom
4. Quantum Field Theory
5. Group Theory and the Noether Theorem
6. Scattering Theory and Feynman Graphs
7. Quantum Electrodynamics
8. Dimensional Regularization
9. Dyson-Schwinger Equations
APPENDIX
Bibliography
Index
1st ed. 1990. 2nd printing 2003 VII, 461
p. Softcover
3-540-00706-7
This is a softcover reprint of the English
translation of 1990 of
the revised and expanded version of Bourbaki's
textbook, Algebre,
Chapters 4 to 7 (1981).
The English translation of the new and expanded
version of
Bourbaki's Algebre, Chapters 4 to 7 completes
Algebra, 1 to 3, by
establishing the theories of commutative
fields and modules over
a principal ideal domain. Chapter 4 deals
with polynomials,
rational fractions and power series. A section
on symmetric
tensors and polynomial mappings between modules,
and a final one
on symmetric functions, have been added.
Chapter 5 has been
entirely rewritten. After the basic theory
of extensions (prime
fields, algebraic, algebraically closed,
radical extension),
separable algebraic extensions are investigated,
giving way to a
section on Galois theory. Galois theory is
in turn applied to
finite fields and abelian extensions. The
chapter then proceeds
to the study of general non-algebraic extensions
which cannot
usually be found in textbooks: p-bases, transcendental
extensions, separability criterions, regular
extensions. Chapter
6 treats ordered groups and fields and based
on it is Chapter 7:
modules over a p.i.d. studies of torsion
modules, free modules,
finite type modules, with applications to
abelian groups and
endomorphisms of vector spaces. Sections
on semi-simple
endomorphisms and Jordan decomposition have
been added.
Chapter IV: Polynomials and Rational Fractions
Chapter V: Commutative Fields
Chapter VI: Ordered Groups and Fields
Chapter VII: Modules Over Principal Ideal
Domains
Contents:
Capter IV: Polinomials and Rational Fractions.-
Chapter V:
Commutative Fields.- Chapter VI: Ordered
Groups and Fields.-
Chapter VII: Modules Over Principal Ideal
Domains.
2003 XVI, 357 p. Softcover
3-540-00838-1
The role of singular trajectories in control
theory is analysed
in this volume that contains about 60 exercises
and problems. A
section is devoted to the applications of
singular trajectories
to the optimisation of batch reactors. The
theoretical part based
on the Martinet case concerns the singularity
analysis of
singular trajectories in sub-Riemannian geometry.
An algorithm is
given to evaluate conjugate points and a
final chapter discusses
open problems. The volume will interest mathematicians
and
engineers.
Series: Mathematiques et Applications. Vol..
40
2003 XI, 260 p. 83 illus. Softcover
1-85233-733-8
Complex analysis is one of the most attractive
of all the core
topics in an undergraduate mathematics course.
Its importance to
applications means that it can be studied
both from a very pure
perspective and a very applied perspective.
This book takes
account of these varying needs and backgrounds
and provides a
self-study text for students in mathematics,
science and
engineering. Beginning with a summary of
what the student needs
to know at the outset, it covers all the
topics likely to feature
in a first course in the subject, including:
complex numbers
differentiation integration Cauchy's theorem
and its consequences
Laurent series and the residue theorem applications
of contour
integration conformal mappings and harmonic
functions A brief
final chapter explains the Riemann hypothesis,
the most
celebrated of all the unsolved problems in
mathematics, and ends
with a short descriptive account of iteration,
Julia sets and the
Mandelbrot set. Clear and careful explanations
are backed up with
worked examples and more than 100 exercises,
for which full
solutions are provided.
Series: Springer Undergraduate Mathematics
Series.
2003 XII, 270 p. 90 illus. Softcover
1-85233-708-7
This book, derived from an innovative course
of lectures, is a
first introduction to the mathematical description
of fields,
flows and waves. It shows students, early
in their studies, how
many of the topics they have encountered
are useful in
constructing, analysing and interpreting
phenomena in the real
world. Designed for second-year undergraduate
students in
mathematics, mathematical physics, and engineering,
it presumes
only a limited familiarity with several variable
calculus and
vector fields. It develops the concepts of
flux, conservation law
and boundary value problem through simple
examples of heat flow,
electric potentials and gravitational fields.
The ideas are
developed through worked examples, and a
range of exercises (with
solutions) is provided to test understanding.
Chapters 1-7
contain ample material for an introductory
lecture course, while
later chapters on waves in fluids, solids
and electromagnetism,
and on bio-mathematics, show how the extension
of earlier ideas
leads to the description and explanation
of important topics in
modern technology and science.
Contents: Preface.- The Continuum Description.-
Unsteady Heat
Flow.- Fields and Potentials.- Laplace's
Equation and Poisson's
Equation.- Motion of an Elastic String.-
Fluid Flow.- Elastic
Deformations.- Vibrations and Waves.- Electromagnetic
Waves and
Light.- Chemical and Biological Models.-
Solutions.- Bibliography.-
Index
Series: Springer Undergraduate Mathematics
Series.