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With a fresh geometric approach that incorporates more than 250
illustrations, this textbook sets itself apart from all others in
advanced calculus. Besides the classical capstones--the change of
variables formula, implicit and inverse function theorems, the
integral theorems of Gauss and Stokes--the text treats other
important topics in differential analysis, such as Morse's lemma
and the Poincare lemma. The ideas behind most topics can be
understood with just two or three variables. The book incorporates
modern computational tools to give visualization real power. Using
2D and 3D graphics, the book offers new insights into fundamental
elements of the calculus of differentiable maps. The geometric
theme continues with an analysis of the physical meaning of the
divergence and the curl at a level of detail not found in other
advanced calculus books. This is a textbook for undergraduates and
graduate students in mathematics, the physical sciences, and
economics. Prerequisites are an introduction to linear algebra and
multivariable calculus. There is enough material for a year-long
course on advanced calculus and for a variety of semester
courses--including topics in geometry. The measured pace of the
book, with its extensive examples and illustrations, make it
especially suitable for independent study.
In 1905, Albert Einstein offered a revolutionary theory--special
relativity--to explain some of the most troubling problems in
current physics concerning electromagnetism and motion. Soon
afterwards, Hermann Minkowski recast special relativity essentially
as a new geometric structure for spacetime. These ideas are the
subject of the first part of the book. The second part develops the
main implications of Einstein's general relativity as a theory of
gravity rooted in the differential geometry of surfaces. The author
explores the way an individual observer views the world and how a
pair of observers collaborate to gain objective knowledge of the
world. To encompass both the general and special theory, he uses
the geometry of spacetime as the unifying theme of the book. To
read it, one needs only a first course in linear algebra and
multivariable calculus and familiarity with the physical
applications of calculus.
In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.
With a fresh geometric approach that incorporates more than 250
illustrations, this textbook sets itself apart from all others in
advanced calculus. Besides the classical capstones--the change of
variables formula, implicit and inverse function theorems, the
integral theorems of Gauss and Stokes--the text treats other
important topics in differential analysis, such as Morse's lemma
and the Poincare lemma. The ideas behind most topics can be
understood with just two or three variables. The book incorporates
modern computational tools to give visualization real power. Using
2D and 3D graphics, the book offers new insights into fundamental
elements of the calculus of differentiable maps. The geometric
theme continues with an analysis of the physical meaning of the
divergence and the curl at a level of detail not found in other
advanced calculus books. This is a textbook for undergraduates and
graduate students in mathematics, the physical sciences, and
economics. Prerequisites are an introduction to linear algebra and
multivariable calculus. There is enough material for a year-long
course on advanced calculus and for a variety of semester
courses--including topics in geometry. The measured pace of the
book, with its extensive examples and illustrations, make it
especially suitable for independent study.
This book provides a broad analysis of the policy, programmatic, and research issues surrounding managed care services delivery systems that provide the majority of health and behavioral health care services in the United States. By including an interdisciplinary group of authors and addressing multiple fields of practice including health care, gerontology, child welfare, substance abuse, and mental health, the editors provide a broad overview of "macro" managed care issues.
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