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The last treatise on the theory of determinants, by T. Muir, revised and enlarged by W. H. Metzler, was published by Dover Publications Inc. in 1960. It is an unabridged and corrected republication of the edition ori- nally published by Longman, Green and Co. in 1933 and contains a preface by Metzler dated 1928. The Table of Contents of this treatise is given in Appendix 13. A small number of other books devoted entirely to determinants have been published in English, but they contain little if anything of importance that was not known to Muir and Metzler. A few have appeared in German and Japanese. In contrast, the shelves of every mathematics library groan under the weight of books on linear algebra, some of which contain short chapters on determinants but usually only on those aspects of the subject which are applicable to the chapters on matrices. There appears to be tacit agreement among authorities on linear algebra that determinant theory is important only as a branch of matrix theory. In sections devoted entirely to the establishment of a determinantal relation, many authors de?ne a determinant by ?rst de?ning a matrixM and then adding the words: “Let detM be the determinant of the matrix M” as though determinants have no separate existence. This belief has no basis in history.

Algebra --- Determinants. --- Mathematical physics. --- Déterminants (Mathématiques) --- Physique mathématique --- Mathematical physics --- Determinants --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematical Theory --- Applied Physics --- Mathematics. --- Matrix theory. --- Algebra. --- Physics. --- Linear and Multilinear Algebras, Matrix Theory. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Mathematical analysis --- Resultants

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This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub­ stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica­ tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com­ plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.

517.95 --- Partial differential equations --- 517.95 Partial differential equations --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Mathematical physics. --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis

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The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced anal­ ysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.

Quantum theory --- Linear operators --- Mathematical physics --- Quantum theory. --- Linear operators. --- Mathematical physics. --- 530 --- Linear maps --- Maps, Linear --- Operators, Linear --- Quantum mechanics. Quantumfield theory --- Differential geometry. Global analysis --- Functional analysis. --- Quantum physics. --- Functional Analysis. --- Theoretical, Mathematical and Computational Physics. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics

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Canonical Perturbation Theories, Degenerate Systems and Resonance presents the foundations of Hamiltonian Perturbation Theories used in Celestial Mechanics, emphasizing the Lie Series Theory and its application to degenerate systems and resonance. This book is the complete text on the subject including advanced topics in Hamiltonian Mechanics, Hori’s Theory, and the classical theories of Poincaré, von Zeipel-Brouwer, and Delaunay. Also covered are Kolmogorov’s frequency relocation method to avoid small divisors, the construction of action-angle variables for integrable systems, and a complete overview of some problems in Classical Mechanics. Sylvio Ferraz-Mello makes these ideas accessible not only to Astronomers, but also to those in the related fields of Physics and Mathematics.

Perturbation (Astronomy) --- Series, Lie. --- Hamiltonian systems. --- resonance hamiltonian methods in celestial mechanics and applications --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Lie series --- Functions of complex variables --- Celestial mechanics --- Perturbation (Mathematics) --- Mathematics. --- Astrophysics and Astroparticles. --- Theoretical, Mathematical and Computational Physics. --- Astronomy, Observations and Techniques. --- Applications of Mathematics. --- Math --- Science --- Astrophysics. --- Mathematical physics. --- Observations, Astronomical. --- Astronomy—Observations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Astronomical observations --- Observations, Astronomical --- Physical mathematics --- Physics --- Astronomical physics --- Astronomy --- Cosmic physics --- Mathematics

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Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented. Essential problem sets between the chapters also aid the retention of the new material and for the consolidation of material learned in previous chapters. The text and problem sets have proved a useful springboard for the application of the basic material presented here to topics in semiconductor physics, and the physics of carbon-based nanostructures.

Condensed matter. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Mathematical physics. --- Optical materials. --- Condensed Matter Physics. --- Group Theory and Generalizations. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Optical and Electronic Materials. --- Optics --- Materials --- Physical mathematics --- Physics --- Mathematics --- Physics. --- Electronic materials. --- Electronic materials --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groupes, Théorie des. --- Matière condensée. --- Group theory --- Solid state physics