Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts (Modern Birkhauser Classics)

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9780817683399: Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts (Modern Birkhauser Classics)
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Book by Arnold VI GuseinZade SM Varchenko Alexander N

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Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science.  The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level.  With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.

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Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners.

Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications.

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V.I. Arnold; S.M. Gusein-Zade; Alexander N. Varchenko
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V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
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Descripción BIRKHAUSER BOSTON INC, United States, 2012. Paperback. Condición: New. 2012 ed.. Language: English . Brand New Book. â Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book s sophisticated development permits readers to explore more applications than previous books on singularities. Nº de ref. del artículo: AAZ9780817683399

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V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
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Descripción BIRKHAUSER BOSTON INC, United States, 2012. Paperback. Condición: New. 2012 ed.. Language: English . Brand New Book. â Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book s sophisticated development permits readers to explore more applications than previous books on singularities. Nº de ref. del artículo: AAZ9780817683399

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V.I. Arnold (author), S.M. Gusein-Zade (author), Alexander N. Varchenko (author)
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Descripción Birkhäuser Boston 2012-05-23, New York, 2012. paperback. Condición: New. Nº de ref. del artículo: 9780817683399

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Descripción Birkhauser Boston Inc. Paperback. Condición: New. New copy - Usually dispatched within 2 working days. Nº de ref. del artículo: B9780817683399

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Descripción BIRKHAUSER BOSTON INC, United States, 2012. Paperback. Condición: New. 2012 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. â Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book s sophisticated development permits readers to explore more applications than previous books on singularities. Nº de ref. del artículo: LIE9780817683399

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V. I. Arnold
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Arnold, V. I. / Gusein-Zade, S. M.
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Descripción Condición: New. Publisher/Verlag: Springer, Basel | Classification of Critical Points, Caustics and Wave Fronts | This first of two volumes deals with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities, beginning at a basic level that presupposes a limited mathematical background. | Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it available and affordable to a global audience of researchers and practitioners.Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications. | Part I. Basic concepts.- The simplest examples.- The classes Sigma^ I .- The quadratic differential of a map.- The local algebra of a map and the Weierstrass preparation theorem.- The local multiplicity of a holomorphic map.- Stability and infinitesimal stability.- The proof of the stability theorem.- Versal deformations.- The classification of stable germs by genotype.- Review of further results.- Part II. Critical points of smooth functions.- A start to the classification of critical points.- Quasihomogeneous and semiquasihomogeneous singularities.- The classification of quasihomogeneous functions.- Spectral sequences for the reduction to normal forms.- Lists of singularities.- The determinator of singularities.- Real, symmetric and boundary singularities.- Part III. Singularities of caustics and wave fronts.- Lagrangian singularities.- Generating families.- Legendrian singularities.- The classification of Lagrangian and Legendrian singularities.- The bifurcation of caustics and wave fronts.- References.- Further references.- Subject Index. | Format: Paperback | Language/Sprache: english | 604 gr | 282 pp. Nº de ref. del artículo: K9780817683399

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V.I. ARNOLD
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Descripción BirkhÇÏuser, 2012. Paperback. Condición: NEW. 9780817683399 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Nº de ref. del artículo: HTANDREE0286081

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