Manfredo P Do Carmo Selected Papers

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Manfredo P. do Carmo – Selected Papers

Author : Manfredo P. do Carmo
Publisher : Springer Science & Business Media
ISBN 13 : 3642255884
Total Pages : 492 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Manfredo P. do Carmo – Selected Papers by : Manfredo P. do Carmo

Download or read book Manfredo P. do Carmo – Selected Papers written by Manfredo P. do Carmo and published by Springer Science & Business Media. This book was released on 2012-04-02 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.

Manfredo P. do Carmo – Selected Papers

Author : Manfredo do Carmo
Publisher : Springer
ISBN 13 : 9783642255892
Total Pages : 497 pages
Book Rating : 4.2/5 (558 download)

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Book Synopsis Manfredo P. do Carmo – Selected Papers by : Manfredo do Carmo

Download or read book Manfredo P. do Carmo – Selected Papers written by Manfredo do Carmo and published by Springer. This book was released on 2012-04-07 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.

Differential Forms and Applications

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
ISBN 13 : 3642579515
Total Pages : 124 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Differential Forms and Applications by : Manfredo P. Do Carmo

Download or read book Differential Forms and Applications written by Manfredo P. Do Carmo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Differential Geometry Of Curves And Surfaces

Author : Masaaki Umehara
Publisher : World Scientific Publishing Company
ISBN 13 : 9814740268
Total Pages : 327 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Differential Geometry Of Curves And Surfaces by : Masaaki Umehara

Download or read book Differential Geometry Of Curves And Surfaces written by Masaaki Umehara and published by World Scientific Publishing Company. This book was released on 2017-05-12 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.

Elementary Differential Geometry

Author : A.N. Pressley
Publisher : Springer Science & Business Media
ISBN 13 : 1848828918
Total Pages : 469 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Elementary Differential Geometry by : A.N. Pressley

Download or read book Elementary Differential Geometry written by A.N. Pressley and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul

Global Analysis

Author : Ilka Agricola
Publisher : American Mathematical Soc.
ISBN 13 : 0821829513
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Global Analysis by : Ilka Agricola

Download or read book Global Analysis written by Ilka Agricola and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.

An Introduction To Chaotic Dynamical Systems

Author : Robert Devaney
Publisher : CRC Press
ISBN 13 : 0429981937
Total Pages : 251 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis An Introduction To Chaotic Dynamical Systems by : Robert Devaney

Download or read book An Introduction To Chaotic Dynamical Systems written by Robert Devaney and published by CRC Press. This book was released on 2018-03-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

Riemannian Geometry

Author : Manfredo P. do Carmo
Publisher : Copernicus
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Riemannian Geometry by : Manfredo P. do Carmo

Download or read book Riemannian Geometry written by Manfredo P. do Carmo and published by Copernicus. This book was released on 1992 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

Introduction to Riemannian Manifolds

Author : John M. Lee
Publisher : Springer
ISBN 13 : 3319917552
Total Pages : 437 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Introduction to Riemannian Manifolds by : John M. Lee

Download or read book Introduction to Riemannian Manifolds written by John M. Lee and published by Springer. This book was released on 2019-01-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Curves and Surfaces

Author : Sebastián Montiel
Publisher : American Mathematical Soc.
ISBN 13 : 0821847635
Total Pages : 395 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Curves and Surfaces by : Sebastián Montiel

Download or read book Curves and Surfaces written by Sebastián Montiel and published by American Mathematical Soc.. This book was released on 2009 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.

Differential Geometry

Author : Erwin Kreyszig
Publisher : Courier Corporation
ISBN 13 : 0486318621
Total Pages : 384 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Differential Geometry by : Erwin Kreyszig

Download or read book Differential Geometry written by Erwin Kreyszig and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Invitation to Dynamical Systems

Author : Edward R. Scheinerman
Publisher : Courier Corporation
ISBN 13 : 0486275329
Total Pages : 408 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Invitation to Dynamical Systems by : Edward R. Scheinerman

Download or read book Invitation to Dynamical Systems written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-05-13 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Visual Differential Geometry and Forms

Author : Tristan Needham
Publisher : Princeton University Press
ISBN 13 : 0691203709
Total Pages : 530 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Visual Differential Geometry and Forms by : Tristan Needham

Download or read book Visual Differential Geometry and Forms written by Tristan Needham and published by Princeton University Press. This book was released on 2021-07-13 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

A Course on Rough Paths

Author : Peter K. Friz
Publisher : Springer Nature
ISBN 13 : 3030415562
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course on Rough Paths by : Peter K. Friz

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Differential Geometry of Curves and Surfaces

Author : Kristopher Tapp
Publisher : Springer
ISBN 13 : 3319397990
Total Pages : 370 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Differential Geometry of Curves and Surfaces by : Kristopher Tapp

Download or read book Differential Geometry of Curves and Surfaces written by Kristopher Tapp and published by Springer. This book was released on 2016-09-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

Analysis On Manifolds

Author : James R. Munkres
Publisher : CRC Press
ISBN 13 : 042996269X
Total Pages : 381 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Analysis On Manifolds by : James R. Munkres

Download or read book Analysis On Manifolds written by James R. Munkres and published by CRC Press. This book was released on 2018-02-19 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

Elements of Differential Geometry

Author : Richard S. Millman
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Elements of Differential Geometry by : Richard S. Millman

Download or read book Elements of Differential Geometry written by Richard S. Millman and published by Prentice Hall. This book was released on 1977 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for an advanced undergraduate (having taken linear algebra and multivariable calculus). It provides the necessary background for a more abstract course in differential geometry. The inclusion of diagrams is done without sacrificing the rigor of the material. For all readers interested in differential geometry.