This textbook is intended for a one-semester undergraduate course in the differential geometry of curves and surfaces, assuming only multivariable calculus and linear algebra. The book culminates with the celebrated Gauss-Bonnet Theorem and applications to spherical and hyperbolic geometry. Online interactive computer graphics applets coordinated with each section form an integral part of the exposition. The applets allow teachers and students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena. Each section includes numerous interesting exercises that range from straightforward to challenging.
Details
ISBN: 978-1-56881-456-8
Year: 2010
Format: Hardcover
Pages: 200
Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing.
Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes.
Details
Expected release: April 2010
ISBN: 978-1-56881-426-1
Format: Hardcover
Pages: approx. 250
Intended for undergraduate or beginning graduate students and assuming only prior knowledge of multivariable calculus and linear algebra, this book introduces classical differential geometry of curves and surfaces and proceeds seamlessly to the modern theory of manifolds. The first part of the book introduces the local and global theories of plane curves and then space curves. The middle part studies the extrinsic and intrinsic geometry of regular surfaces, including the Theorema Egregium and the Gauss-Bonnet Theorem. The final chapters develop the notion of a differentiable manifold, study Riemannian manifolds and conclude with applications of manifolds to physics. Online interactive and extensible computer graphics applets enhance the exposition by developing an intuition for the concepts and allowing one to explore the examples. Collections of exercises at the end of each section and appendices on useful topology and linear algebra background make this book ideal for self-study or use as a textbook.
Details
Expected release: May 2010
ISBN: 978-1-56881-457-5
Format: Hardcover
Pages: approx. 450
Hardback (ISBN-13: 9780883857649)
89 b/w illus.
Page extent: 324 pages
Size: 254 x 178 mm
Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool. This second edition has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.
* Exercises interspersed in the text, with detailed solutions, allow students to test their understanding * Covers the standard material on complex analysis whilst also discussing intriguing additional topics * Topics are discussed in commonly encountered terms, rather than in a general, abstract setting
Preface; 1. From complex numbers to Cauchy's Theorem; 2. Applications of Cauchy's Theorem; 3. Analytic continuation; 4. Harmonic functions and conformal mapping; 5. Miscellaneous topics; Index.
Hardback (ISBN-13: 9780521883467)
21 b/w illus.
Page extent: 232 pages
Size: 247 x 174 mm
Why did Einstein tirelessly study unified field theory for more than 30 years* In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science.
* The first book to approach the subject of Einsteinfs study of unified field theory from both historical and philosophical perspectives * Provides a coherent view of Einsteinfs development as a scientist, highlighting the link between the general theory of relativity and unified field theory * Discusses topics of Einsteinfs science that have not yet been covered in a single book
Introduction; 1. Formulating the gravitational field equations; 2. On the method of theoretical physics; 3. Unification and field theory; 4. Experiment and experience; 5. The method as directive: semivectors; 6. Unification in five dimensions; 7. The method and the quantum; Conclusion; Bibliography; Index.