Geometric Integration Theory


Author: Steven G. Krantz,Harold R. Parks
Publisher: Springer Science & Business Media
ISBN: 9780817646790
Category: Mathematics
Page: 340
View: 4158
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This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Geometric Integration Theory


Author: Steven G. Krantz,Harold R. Parks
Publisher: Springer Science & Business Media
ISBN: 9780817646790
Category: Mathematics
Page: 340
View: 7499
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This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Geometric Measure Theory


Author: Herbert Federer
Publisher: Springer
ISBN: 3642620108
Category: Mathematics
Page: 677
View: 3493
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"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)

Computation and Visualization of Geometric Partial Differential Equations


Author: Christopher Tiee
Publisher: Lulu.com
ISBN: 1329440730
Category:
Page: N.A
View: 3360
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A Course in Metric Geometry


Author: Dmitri Burago,I͡Uriĭ Dmitrievich Burago,Sergeĭ Ivanov
Publisher: American Mathematical Soc.
ISBN: 0821821296
Category: Mathematics
Page: 415
View: 7602
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``Metric geometry'' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ``easy-to-touch'' mathematical objects using ``easy-to-visualize'' methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations


Author: Jared Speck
Publisher: American Mathematical Soc.
ISBN: 1470428571
Category: Differential equations, Nonlinear
Page: 515
View: 2889
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In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-data solutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics, hyperbolic conservation laws, wave equations, and geometric analysis.

A Course in Minimal Surfaces


Author: Tobias H. Colding,William P. Minicozzi
Publisher: American Mathematical Soc.
ISBN: 0821853236
Category: Mathematics
Page: 313
View: 2683
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Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

Symmetries and Integrability of Difference Equations


Author: Decio Levi,Peter Olver,Zora Thomova,Pavel Winternitz
Publisher: Cambridge University Press
ISBN: 1139493841
Category: Mathematics
Page: N.A
View: 3127
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Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.

Seminar on geometric measure theory


Author: Robert Hardt,León Simón
Publisher: Birkhauser
ISBN: 9783764318154
Category: Mathematics
Page: 117
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An Introduction to Measure and Integration


Author: Inder K. Rana
Publisher: American Mathematical Soc.
ISBN: 9780821883914
Category: Lebesgue integral
Page: 424
View: 1808
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Basic Real Analysis


Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644415
Category: Mathematics
Page: 656
View: 3581
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Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

Geometric Asymptotics


Author: Victor Guillemin,Shlomo Sternberg
Publisher: American Mathematical Soc.
ISBN: 0821816330
Category: Mathematics
Page: 480
View: 7956
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Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years - the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence.

Integration Theory

With Special Attention to Vector Measures
Author: Klaus Bichteler
Publisher: Springer
ISBN: 3540383697
Category: Mathematics
Page: 360
View: 5434
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Differential Geometrical Theory of Statistics


Author: Frédéric Barbaresco,Frank Nielsen
Publisher: MDPI
ISBN: 3038424242
Category: Computers
Page: 472
View: 6767
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This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy

Geometric Optimal Control

Theory, Methods and Examples
Author: Heinz Schättler,Urszula Ledzewicz
Publisher: Springer Science & Business Media
ISBN: 1461438349
Category: Mathematics
Page: 640
View: 9667
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This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Matrix Analysis


Author: Roger A. Horn,Charles R. Johnson
Publisher: Cambridge University Press
ISBN: 9780521386326
Category: Mathematics
Page: 561
View: 8158
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In this book the authors present classical and recent results for matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematics, and the necessary material has only occurred sporadically in the literature and university curricula. As the interest in applied mathematics has grown, the need for a text and a reference work offering a broad selection of topics has become apparent, and this book aims to meet that need. This book will be welcomed as an undergraduate or graduate textbook for students studying matrix analysis. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. They begin with a review and discussion of eigenvalues and eigenvectors. The following chapters each treat a major topic in depth. This volume should be useful not only as a text, but also as a self-contained reference work to a variety of audiences in other scientific fields.

Mathematical Olympiad Treasures


Author: Titu Andreescu,Bogdan Enescu
Publisher: Springer Science & Business Media
ISBN: 9780817682538
Category: Mathematics
Page: 253
View: 4960
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Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.

The Elements of Integration and Lebesgue Measure


Author: Robert G. Bartle
Publisher: John Wiley & Sons
ISBN: 1118626125
Category: Mathematics
Page: 179
View: 8309
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Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.

Cornerstones of Cost Management


Author: Don R. Hansen,Maryanne M. Mowen
Publisher: Cengage Learning
ISBN: 1305970667
Category: Business & Economics
Page: 1120
View: 1781
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Hansen/Mowen’s CORNERSTONES OF COST MANAGEMENT, 4E demonstrates the dynamic nature of cost accounting in today’s changing business environment. The book covers functional-based cost and control, and then activity-based cost systems, giving students the skills to manage any cost management system. Developed using extensive research on student learning behavior, this book presents concepts in a unique format that speaks to how students learn. Cornerstones examples in each chapter emphasize the How, Why, and What-Ifs of basic cost management concepts, while delving into the conceptual nature of each equation or topic. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.