This text breaks new ground in presenting and applying
sophisticated mathematics in an elementary setting. Aimed at
physics students, it covers the theory and physical applications of
linear algebra and of the calculus of several variables,
particularly the exterior calculus. The exterior differential
calculus is now being recognized by mathematicians and physicists
as the best method of formulating the geometrical laws of physics,
and the frontiers of... more...

There are a number of excellent texts available on semi-classical
analysis. The focus of the present monograph, however, is an aspect
of the subject somewhat less systematically developed in other
texts: In semi-classical analysis, many of the basic results
involve asymptotic expansions in which the terms can be computed by
symbolic techniques, and the focus of this monograph is the “symbol
calculus” created thus. In particular, the techniques... more...

Multiplicity diagrams can be viewed as schemes for describing the
phenomenon of "symmetry breaking" in quantum physics. The subject
of this book is the multiplicity diagrams associated with the
classical groups U(n), O(n), etc. It presents such topics as
asymptotic distributions of multiplicities, hierarchical patterns
in multiplicity diagrams, lacunae, and the multiplicity diagrams of
the rank 2 and rank 3 groups. The authors take a novel approach,... more...

Symplectic geometry is very useful for formulating clearly and
concisely problems in classical physics and also for understanding
the link between classical problems and their quantum counterparts.
It is thus a subject of interest to both mathematicians and
physicists, though they have approached the subject from different
viewpoints. This is the first book that attempts to reconcile these
approaches. The authors use the uncluttered, coordinate-free... more...

This original Dover textbook is based on an advanced
undergraduate course taught by the author for more than
50 years. It introduces semi-Riemannian geometry
and its principal physical application, Einstein's theory of
general relativity, using the Cartan exterior calculus as a
principal tool. Prerequisites include linear algebra and
advanced calculus. 2012 edition.

This textbook, available in two volumes, has been developed from a
course taught at Harvard over the last decade. The course covers
principally the theory and physical applications of linear algebra
and of the calculus of several variables, particularly the exterior
calculus. The authors adopt the 'spiral method' of teaching,
covering the same topic several times at increasing levels of
sophistication and range of application. Thus the reader develops... more...

This text breaks new ground in presenting and applying
sophisticated mathematics in an elementary setting. Aimed at
physics students, it covers the theory and physical applications of
linear algebra and of the calculus of several variables,
particularly the exterior calculus. The exterior differential
calculus is now being recognized by mathematicians and physicists
as the best method of formulating the geometrical laws of physics,
and the frontiers of... more...

A pioneer in the field of dynamical systems created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides and MATLAB exercises. 2010 edition.

This book discusses the equivariant cohomology theory of differentiable manifolds. Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph. It covers almost all important aspects of the subject The authors are key authorities in this field.