Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.

Large Deviations and Applications (CBMS-NSF Regional Conference Series in Applied Mathematics, No. 46)

Science & Math

Varadhan, S.R.S.

Mathematics

Society for Industrial & Applied Mathematics

Ten Lectures on the Probabilistic Method (Cbms-Nsf Regional Conference Series in Applied Mathematics, No 52)

Joel Spencer

The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. 
As part of the algorithm, Gardner introduces several major new techniques. In particular, the use of Cartan's idea of principal components that appears in his theory of Repere Mobile, and the use of Lie algebras instead of Lie groups, effectively a linear procedure, provide a tremendous simplification. One must, however, know how to convert from one to the other, and the author provides the Rosetta stone to accomplish this. In complex problems, it is essential to be able to identify natural blocks in group actions and not just individual elements, and prior to this publication, there was no reference to block matrix techniques.
The Method of Equivalence and Its Applications details ten diverse applications including Lagrangian field theory, control theory, ordinary differential equations, and Riemannian and conformal geometry.
This volume contains a series of lectures, the purpose of which was to describe the equivalence algorithm and to show, in particular, how it is applied to several pedagogical examples and to a problem in control theory called state estimation of plants under feedback. The lectures, and hence the book, focus on problems in real geometry. 
Special Features:
- only book to treat this subject in such depth and to include the algorithm, the use of principal components, and the use of infinitesimal analysis on the Lie algebra level.
Audience:
The reader should possess a background in calculus on manifolds and a familiarity with abstract linear and multilinear algebra. A first course on manifolds with an introduction to Lie groups and the ability to believe advanced results would be even more helpful. This volumes contains asides at various levels involving representation theory of Lie groups and Lie algebras, exterior differential systems, and Lie pseudo-groups.

The Method of Equivalence and Its Applications (CBMS-NSF Regional Conference Series in Applied Mathematics, No. 58)

Gardner, Robert B.

Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices - symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum-maximum characterization of characteristic roots, Kronecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools.

Introduction to Matrix Analysis (Classics in Applied Mathematics, Vol 12)

Richard Bellman

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory - some of which are nontrivial - have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors.
 Tensor Analysis is unique in that it is the first book to cover these three subject areas: the spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.
 Audience: The intended audience is researchers and graduate students.
 Contents:List of Figures; List of Algrithms; Chapter 1: Introduction; Chapter 2: Eigenvalues of Tensors; Chapter 3: Nonnegative Tensors; Chapter 4: Spectral Hypergraph Theory via Tensors; Chapter 5: Positive Semidefinite Tensors; Chapter 6: Completely Positive Tensors and Copositive Tensors; Bibliography; Index.

Tensor Analysis: Spectral Theory and Special Tensors

Liqun Qi

Ziyan Luo

Printed in Asia - Carries Same Contents as of US edition - Opt Expedited Shipping for 3 to 4 day delivery -

Numerical Computing with MATLAB, Revised Reprint

Moler

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