Skip to content
## Elementary Differential Geometry, Revised 2nd Edition

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. Over 36,000 copies sold worldwide Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study Extensive update of appendices on Mathematica and Maple software packages Thorough streamlining of second edition's numbering system Fuller information on solutions to odd-numbered problems Additional exercises and hints guide students in using the latest computer modeling tools
## Elementary Differential Geometry

Written primarily for readers who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Second Edition provides an introduction to the geometry of curves and surfaces. Although the popular First Edition has been extensively modified, this Second Edition maintains the elementary character of that volume, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis has been placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. For readers with access to the symbolic computation programs, Mathematica or Maple, the book includes approximately 30 optional computer exercises. These are not intended as an essential part of the book, but rather an extension. No computer skill is necessary to take full advantage of this comprehensive text. * Gives detailed examples for all essential ideas * Provides more than 300 exercises * Features more than 200 illustrations * Includes an introduction to using computers, and supplies answers to computer exercises given for both Mathematica and Maple systems
## Visual Differential Geometry and Forms

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.
## Studyguide for Elementary Differential Geometry, Revised 2nd Edition by Oneill, Barrett

Never HIGHLIGHT a Book Again Includes all testable terms, concepts, persons, places, and events. Cram101 Just the FACTS101 studyguides gives all of the outlines, highlights, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanies: 9780872893795. This item is printed on demand.
## Studyguide for Elementary Differential Geometry, Revised 2nd Edition by Barrett Oneill, Isbn 9780120887354

Never HIGHLIGHT a Book Again! Virtually all of the testable terms, concepts, persons, places, and events from the textbook are included. Cram101 Just the FACTS101 studyguides give all of the outlines, highlights, notes, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanys: 9780120887354 .
## Machine Vision and Navigation

This book presents a variety of perspectives on vision-based applications. These contributions are focused on optoelectronic sensors, 3D & 2D machine vision technologies, robot navigation, control schemes, motion controllers, intelligent algorithms and vision systems. The authors focus on applications of unmanned aerial vehicles, autonomous and mobile robots, industrial inspection applications and structural health monitoring. Recent advanced research in measurement and others areas where 3D & 2D machine vision and machine control play an important role, as well as surveys and reviews about vision-based applications. These topics are of interest to readers from diverse areas, including electrical, electronics and computer engineering, technologists, students and non-specialist readers. • Presents current research in image and signal sensors, methods, and 3D & 2D technologies in vision-based theories and applications; • Discusses applications such as daily use devices including robotics, detection, tracking and stereoscopic vision systems, pose estimation, avoidance of objects, control and data exchange for navigation, and aerial imagery processing; • Includes research contributions in scientific, industrial, and civil applications.
## Curvature in Mathematics and Physics

As astronaut Donald K. Slayton notes in his Foreword, this chronicle emphasizes the cooperation of "humans on space and on the ground. It realistically balances the role of the highly visible astronaut with the mammoth supporting team." An official NASA publication, Suddenly, Tomorrow Came is profusely illustrated with forty-four figures and tables, plus sixty-three photographs. Historian Paul Dickson brings the narrative up to date with an informative new Introduction.
## 3D Face Modeling, Analysis and Recognition

3D Face Modeling, Analysis and Recognition presentsmethodologies for analyzing shapes of facial surfaces, developscomputational tools for analyzing 3D face data, and illustratesthem using state-of-the-art applications. The methodologies chosenare based on efficient representations, metrics, comparisons, andclassifications of features that are especially relevant in thecontext of 3D measurements of human faces. These frameworks have along-term utility in face analysis, taking into account theanticipated improvements in data collection, data storage,processing speeds, and application scenarios expected as thediscipline develops further. The book covers face acquisition through 3D scanners and 3D facepre-processing, before examining the three main approaches for 3Dfacial surface analysis and recognition: facial curves; facialsurface features; and 3D morphable models. Whilst the focus ofthese chapters is fundamentals and methodologies, the algorithmsprovided are tested on facial biometric data, thereby continuallyshowing how the methods can be applied. Key features: • Explores the underlying mathematics and will apply thesemathematical techniques to 3D face analysis and recognition • Provides coverage of a wide range of applications includingbiometrics, forensic applications, facial expression analysis, andmodel fitting to 2D images • Contains numerous exercises and algorithms throughout thebook
## Recent Progress in Differential Geometry and Its Related Fields

This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information on research papers which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry.
## An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields
## Elementary Differential Geometry

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
## Computing in Euclidean Geometry

This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm. Contents:On the Development of Quantitative Geometry from Phythagoras to Grassmann (W-Y Hsiang)Computational Geometry: A Retrospective (B Chazelle)Mesh Generation and Optimal Triangulation (M Bern & D Eppstein)Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)Randomized Geometric Algorithms (K L Clarkson)The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)Voronoi Diagrams and Delaunay Triangulations (S Fortune)Geometric Constraint Solving in R2 and R3 (C M Hoffmann & P J Vermeer)Polar Forms and Triangular B-Spline Surfaces (H-P Seidel)Computational Geometry and Topological Network Design (J M Smith & P Winter)The Exact Computation Paradigm (C Yap & T Dubé) Readership: Computer scientists and mathematicians. keywords:Computational Geometry;Triangulation;Machine Proof;Randomized Geometric Algorithm;Voronoi Diagram;Delaunay Triangulation;B-Spline;Polar Form;Steiner Tree;Analytic Geometry;Exact Computation Review on First Edition: “The papers are not just summaries; the authors present new material or fresh points of view … I recommend the book to anyone who works in one of the areas surveyed or who is interested in the interaction of Euclidean geometry and computers.” IEEE Parallel & Distributed Technology

eBook in PDF, ePub, Mobi and Kindle Formats