the implicit function theorem history theory and applications modern birkhauser classics

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The Implicit Function Theorem

Author : Steven G. Krantz
ISBN : 9781461459811
Genre : Mathematics
File Size : 84. 75 MB
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The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph. ​ Originally published in 2002, The Implicit Function Theorem is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.​

Advanced Calculus

Author : Harold M. Edwards
ISBN : 0817637079
Genre : Mathematics
File Size : 59. 24 MB
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This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.

Classical Mechanics

Author : Emmanuele DiBenedetto
ISBN : 0817646485
Genre : Mathematics
File Size : 84. 72 MB
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* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

Integration And Modern Analysis

Author : John J. Benedetto
ISBN : 0817646566
Genre : Mathematics
File Size : 70. 93 MB
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This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.

Foundations Of Differentiable Manifolds And Lie Groups

Author : Frank W. Warner
ISBN : 9781475717990
Genre : Mathematics
File Size : 85. 18 MB
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Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Generalized Functions And Fourier Analysis

Author : Michael Oberguggenberger
ISBN : 9783319519111
Genre : Mathematics
File Size : 48. 91 MB
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This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.

Analysis By Its History

Author : Ernst Hairer
ISBN : 9780387770369
Genre : Mathematics
File Size : 65. 52 MB
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This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Bond Graph Model Based Fault Diagnosis Of Hybrid Systems

Author : Wolfgang Borutzky
ISBN : 9783319118604
Genre : Technology & Engineering
File Size : 90. 15 MB
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This book presents bond graph model-based fault detection with a focus on hybrid system models. The book addresses model design, simulation, control and model-based fault diagnosis of multidisciplinary engineering systems. The text beings with a brief survey of the state-of-the-art, then focuses on hybrid systems. The author then uses different bond graph approaches throughout the text and provides case studies.

Mathematical Foundations Of Image Processing And Analysis

Author : Jean-Charles Pinoli
ISBN : 9781118984550
Genre : Technology & Engineering
File Size : 49. 15 MB
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Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridge between the pure and applied mathematical disciplines, and the processing and analysis of gray-tone and binary images. It is accessible to readers who have neither extensive mathematical training, nor peer knowledge in Image Processing and Analysis. It is a self-contained book focusing on the mathematical notions, concepts, operations, structures, and frameworks that are beyond or involved in Image Processing and Analysis. The notations are simplified as far as possible in order to be more explicative and consistent throughout the book and the mathematical aspects are systematically discussed in the image processing and analysis context, through practical examples or concrete illustrations. Conversely, the discussed applicative issues allow the role of mathematics to be highlighted. Written for a broad audience – students, mathematicians, image processing and analysis specialists, as well as other scientists and practitioners – the author hopes that readers will find their own way of using the book, thus providing a mathematical companion that can help mathematicians become more familiar with image processing and analysis, and likewise, image processing and image analysis scientists, researchers and engineers gain a deeper understanding of mathematical notions and concepts.

The Geometry Of Domains In Space

Author : Steven G. Krantz
ISBN : 0817640975
Genre : Mathematics
File Size : 54. 63 MB
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This comprehensive treatment of domains (in space) emphasizes the growing interaction between analysis and geometry. Geometric analysis, as it is known, is currently an important area of study for both pure and applied mathematicians, physicists, and engineers. Aimed at graduate students of the field, this monograph will be useful in the classroom or as a resource for self-study. The prerequisites are minimal; a good understanding of multivariable calculus and linear algebra will suffice for most purposes.

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