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Classroom-tested and lucidly written, Multivariable Calculus gives
a thorough and rigoroustreatment of differential and integral
calculus of functions of several variables. Designed as
ajunior-level textbook for an advanced calculus course, this book
covers a variety of notions,including continuity , differentiation,
multiple integrals, line and surface integrals, differentialforms,
and infinite series. Numerous exercises and examples throughout the
book facilitatethe student's understanding of important
concepts.The level of rigor in this textbook is high; virtually
every result is accompanied by a proof. Toaccommodate teachers'
individual needs, the material is organized so that proofs can be
deemphasizedor even omitted. Linear algebra for n-dimensional
Euclidean space is developedwhen required for the calculus; for
example, linear transformations are discussed for the treatmentof
derivatives.Featuring a detailed discussion of differential forms
and Stokes' theorem, Multivariable Calculusis an excellent textbook
for junior-level advanced calculus courses and it is also usefulfor
sophomores who have a strong background in single-variable
calculus. A two-year calculussequence or a one-year honor calculus
course is required for the most successful use of thistextbook.
Students will benefit enormously from this book's systematic
approach to mathematicalanalysis, which will ultimately prepare
them for more advanced topics in the field.
Classroom-tested and lucidly written, Multivariable Calculus gives
a thorough and rigoroustreatment of differential and integral
calculus of functions of several variables. Designed as
ajunior-level textbook for an advanced calculus course, this book
covers a variety of notions,including continuity , differentiation,
multiple integrals, line and surface integrals, differentialforms,
and infinite series. Numerous exercises and examples throughout the
book facilitatethe student's understanding of important
concepts.The level of rigor in this textbook is high; virtually
every result is accompanied by a proof. Toaccommodate teachers'
individual needs, the material is organized so that proofs can be
deemphasizedor even omitted. Linear algebra for n-dimensional
Euclidean space is developedwhen required for the calculus; for
example, linear transformations are discussed for the treatmentof
derivatives.Featuring a detailed discussion of differential forms
and Stokes' theorem, Multivariable Calculusis an excellent textbook
for junior-level advanced calculus courses and it is also usefulfor
sophomores who have a strong background in single-variable
calculus. A two-year calculussequence or a one-year honor calculus
course is required for the most successful use of thistextbook.
Students will benefit enormously from this book's systematic
approach to mathematicalanalysis, which will ultimately prepare
them for more advanced topics in the field.
This Seminar began in Moscow in November 1943 and has continued
without interruption up to the present. We are happy that with this
vol ume, Birkhiiuser has begun to publish papers of talks from the
Seminar. It was, unfortunately, difficult to organize their
publication before 1990. Since 1990, most of the talks have taken
place at Rutgers University in New Brunswick, New Jersey. Parallel
seminars were also held in Moscow, and during July, 1992, at IRES
in Bures-sur-Yvette, France. Speakers were invited to submit papers
in their own style, and to elaborate on what they discussed in the
Seminar. We hope that readers will find the diversity of styles
appealing, and recognize that to some extent this reflects the
diversity of styles in a mathematical society. The principal aim
was to have interesting talks, even if the topic was not especially
popular at the time. The papers listed in the Table of Contents
reflect some of the rich variety of ideas presented in the Seminar.
Not all the speakers submit ted papers. Among the interesting talks
that influenced the seminar in an important way, let us mention,
for example, that of R. Langlands on per colation theory and those
of J. Conway and J. McKay on sporadic groups. In addition, there
were many extemporaneous talks as well as short discus sions."
This Seminar began in Moscow in November 1943 and has continued
without interruption up to the present. We are happy that with this
vol ume, Birkhiiuser has begun to publish papers of talks from the
Seminar. It was, unfortunately, difficult to organize their
publication before 1990. Since 1990, most of the talks have taken
place at Rutgers University in New Brunswick, New Jersey. Parallel
seminars were also held in Moscow, and during July, 1992, at IRES
in Bures-sur-Yvette, France. Speakers were invited to submit papers
in their own style, and to elaborate on what they discussed in the
Seminar. We hope that readers will find the diversity of styles
appealing, and recognize that to some extent this reflects the
diversity of styles in a mathematical society. The principal aim
was to have interesting talks, even if the topic was not especially
popular at the time. The papers listed in the Table of Contents
reflect some of the rich variety of ideas presented in the Seminar.
Not all the speakers submit ted papers. Among the interesting talks
that influenced the seminar in an important way, let us mention,
for example, that of R. Langlands on per colation theory and those
of J. Conway and J. McKay on sporadic groups. In addition, there
were many extemporaneous talks as well as short discus sions."
This book views multiple target tracking as a Bayesian inference
problem. Within this framework it develops the theory of single
target tracking, multiple target tracking, and likelihood ratio
detection and tracking. In addition to providing a detailed
description of a basic particle filter that implements the Bayesian
single target recursion, this resource provides numerous examples
that involve the use of particle filters. With these examples
illustrating the developed concepts, algorithms, and approaches --
the book helps radar engineers track when observations are
nonlinear functions of target site, when the target state
distributions or measurement error distributions are not Gaussian,
in low data rate and low signal to noise ratio situations, and when
notions of contact and association are merged or unresolved among
more than one target.
Using the Bayesian inference framework, this book enables the
reader to design and develop mathematically sound algorithms for
dealing with tracking problems involving multiple targets, multiple
sensors, and multiple platforms. It shows how non-linear Multiple
Hypothesis Tracking and the Theory of United Tracking are
successful methods when multiple target tracking must be performed
without contacts or association. With detailed examples
illustrating the developed concepts, algorithms, and approaches,
the book helps the reader track when observations are non-linear
functions of target site, when the target state distributions or
measurements error distributions are not Gaussian, when notions of
contact and association are merged or unresolved among more than
one target, and in low data rate and low signal to noise ratio
situations.
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